She has been living with a man for several years and she wants to do Hajj then go back to him
Question

                I formed a relationship with a man who is not of my religion, and I gave myself to him and have lived with him as a wife (without being married) for twelve years. I decided to do Hajj this year. If I do Hajj, will it be permissible for me to carry on living with him and being intimate with him? Please note that I live in North America and such relationships are recognised and are regarded here as being a form of marriage.
Praise be to Allah.
    Firstly: 

    You have to understand that this living together is blatant zina 
    (fornication or adultery) which is a major sin, concerning which there are 
    stern warnings which should act as a deterrent and an admonition to any 
    believing man or woman. These warnings include the following:
1.

    The report narrated by al-Bukhaari (1386), according to which the Prophet 
    (blessings and peace of Allah be upon him) described the punishment of the 
    fornicators or adulterers, among the things that he saw in his dream when 
    two angels came to him: “… Then we moved on until we came to an opening like 
    an oven, the top of which was narrow and the bottom was wide. A fire was lit 
    beneath it and when it flared up, they (the people in that place) rose up 
    until they almost came out, then when it subsided they fell back into it. In 
    it were naked men and women. I said: ‘Who are these?’ They said: ‘Move on,’ 
    so we moved on…” 

    According to another report narrated by him (7047): “We moved on until we 
    came to something like an oven.” He (the narrator) said: I think he said, 
    “in which there was noise and voices. We looked into it and saw in it naked 
    men and women. Flames came to them from beneath them, and when those flames 
    came to them they began to shout. I said to them: ‘Who are these people?’ 
    They said to me: ‘Move on, move on’…” At the end of the hadith it says: “As 
    for the naked men and women who were in a structure like an oven, they were 
    the men and women who committed zina.” 
2.

    Ibn Khuzaymah and Ibn Hibbaan narrated that Abu Umaamah (may Allah be 
    pleased with him) said: I heard the Messenger of Allah (blessings and peace 
    of Allah be upon him) say: ‘Whilst I was sleeping, two men came to me and 
    took hold of my upper arm. They brought me to a rugged mountain and said: 
    ‘Climb up.’ I said: ‘I cannot.’ They said: ‘We will make it easy for you.’ 
    So I climbed up until, when I reached the top of the mountain, I heard loud 
    voices. I said: ‘What are these voices?’ They said: ‘These are the howl of 
    the people of hell.’ Then I was taken further on, and I saw some people who 
    were hanging by their Achilles tendons, with the sides of their mouths cut 
    open and streaming with blood. I said: ‘Who are these?’ He said: ‘These are 
    the people who broke their fast before it was permissible to do so.’” Then 
    he said: May the Jews and the Christians be doomed. Sulaymaan said: I do not 
    know whether Abu Umaamah heard it from the Messenger of Allah (blessings and 
    peace of Allah be upon him) or it was his opinion. “Then he went on, and saw 
    some people whose bodies were greatly swollen and emitted a foul stench, and 
    they looked terrible. I said: ‘Who are these?’ He said: ‘These are the slain 
    disbelievers.’ Then he took me further on, and I saw some people whose 
    bodies were greatly swollen and emitted a foul stench, as if their stench 
    was that of latrines. I said: ‘Who are these?’ He said: ‘These are the men 
    and women who committed zina’…”

    This hadith was classed as saheeh by al-Albaani in Saheeh at-Targheeb 
    wa’t-Tarheeb, no. 2393 
3.

    Allah has ordained that the punishment of the zaani (fornicator) who was not 
    previously married should be one hundred lashes, and the punishment for the 
    one who was previously married should be stoning to death. Allah, may He be 
    exalted, says (interpretation of the meaning):

    “The woman and the man guilty of illegal sexual intercourse, 
    flog each of them with a hundred stripes. Let not pity withhold you in their 
    case, in a punishment prescribed by Allah, if you believe in Allah and the 
    Last Day. And let a party of the believers witness their punishment”

    [an-Noor 24:2]. 

    Muslim narrated in his Saheeh (3199) that the Prophet (blessings and 
    peace of Allah be upon him) said: “In the case of a previously married man 
    [committing zina with] a previously married woman, (the punishment is) one 
    hundred lashes and stoning.” 
So 
    hasten to repent to Allah, may He be exalted, and sever your relationship 
    with this man, and do not be deceived by the fact that Allah, may He be 
    exalted, has been giving you respite, for He gives respite but does not 
    forget, and His punishment, when it comes, is severe and great indeed. He 
    has given you respite for many years – according to what you say in your 
    question – and this is because of His forbearance towards His slaves and His 
    desire that they should be guided, and His rejoicing when they repent. We do 
    not know, by Allah, how you could have lived for so many years with a man 
    and interacted with him as if you are married. If at that time you were far 
    away from Allah and drowning in worldly desires, then perhaps the fact that 
    you are thinking of Hajj is an indication that you want to come back to 
    Allah and save yourself from the Fire, for death is ever near and this world 
    will soon perish, then tomorrow it will be either Paradise or Hell, then 
    whoever is saved from the Fire and admitted to Paradise has attained 
    success. We ask Allah to accept your repentance and make you one of its 
    people. 

    Secondly: 
It 
    is not permissible for you to marry this man unless he declares his Islam 
    and adheres to Islamic rulings, because it is not permissible for a Muslim 
    woman to be the wife of a disbeliever. This is a matter on which there is 
    scholarly consensus, because Allah, may He be exalted, says (interpretation 
    of the meaning):

    “then if you 
    ascertain that they are true believers, send them not back to the 
    disbelievers, they are not lawful (wives) for the disbelievers nor are the 
    disbelievers lawful (husbands) for them”

    [al-Mumtahinah 60:10]

    “And give not 
    (your daughters) in marriage to Al-Mushrikoon till they believe (in Allah 
    Alone) and verily, a believing slave is better than a (free) Mushrik 
    (idolater, etc.), even though he pleases you. Those (Al-Mushrikoon) invite 
    you to the Fire, but Allah invites (you) to Paradise and Forgiveness by His 
    Leave, and makes His Ayat (proofs, evidences, verses, lessons, signs, 
    revelations, etc.) clear to mankind that they may remember”

    [al-Baqarah 2:221]. 

    Marriage to a non-Muslim is not regarded as a marriage; rather it is 
    fornication, sin and an evil deed. 

    You should understand that he is a man whom it is prohibited for you to 
    marry, and you are living with him in an unlawful manner, yet you want to 
    maintain that. This is darkness upon darkness. Save yourself before it is 
    too late. 

    Now you have two options: 

    You can give precedence to Allah, may He be exalted, and seek that which is 
    with Him of eternal happiness and bliss, and a life of ease; or you can give 
    precedence to this sinful life with a man who is not permissible for you, 
    but soon this life will end and you will die and your body will 
    disintegrate, and you will await the reckoning and recompense, at which time 
    the wrongdoer will bite on his hands and say:

    “ ‘Oh! Would 
    that I had taken a path with the Messenger (Muhammad (blessings and peace of 
    Allah be upon him)),

    ‘Ah! Woe to me! Would that I had never taken so-and-so as a 
    friend!

    ‘He indeed led me astray from the Reminder (this Quran) after 
    it had come to me. And Shaitan (Satan) is ever a deserter to man in the hour 
    of need!’”

    [al-Furqaan 25:27-29]. 

    One dip in the fire of Hell is enough to guarantee that one will forget all 
    the pleasures of this life, no matter how great they were. 

    Muslim (2807) narrated that Anas ibn Maalik said: The Messenger of Allah 
    (blessings and peace of Allah be upon him) said: “The most affluent of the 
    people in this world, of those who will go to Hell, will be brought on the 
    Day of Resurrection and dipped once in the Fire. Then it will be said: O son 
    of Adam, did you ever see anything good? Did you ever have any pleasure? He 
    will say: No, by Allah, O Lord. Then the most destitute of the people in 
    this world, of those who will enter Paradise, will be brought and dipped 
    once in Paradise, and it will be said to him: O son of Adam, did you ever 
    see anything bad? Did you ever experience any hardship? He will say: No, by 
    Allah, O Lord. I never saw anything bad and I never experienced any 
    hardship.” 

    Thirdly: 

    The most serious thing that may befall the one who persists in sin is that a 
    seal will be placed on his heart, he will be prevented from repenting and a 
    bad end will be decreed for him. We ask Allah to keep us safe and sound. 

    Some of the sinners delay repentance and procrastinate about the decision to 
    give up their sin, thinking that they will repent at the end of their lives, 
    but then they are prevented from doing so, so they die in a state of sin and 
    they meet Allah in a state of misguidance, and they regret it at a time when 
    regret is of no benefit. 
So 
    our advice to you is to come back to Allah and begin to obey Him; humble 
    yourself before Him and shed tears of repentance and regret. Ask Him and 
    call upon Him a great deal to accept your repentance, forgive your sin and 
    pardon your errors, for He, may He be glorified, loves those who repent, 
    brings close to Him those who ask for forgiveness, and He rejoices over 
    those who turn back to Him. “Know they not that Allah accepts repentance 
    from His slaves and takes the Sadaqat (alms, charities) and that Allah Alone 
    is the One Who forgives and accepts repentance, Most Merciful?” [at-Tawbah 
    9:104]. 

    May Allah protect you from all evil, divert from you all immoral deeds, and 
    bring you back safely to Him. 

    And Allah knows best.