He had a customary marriage with her (zawaaj ‘urfi) then he left her and ran away!
Question

I knew a man who deceived me by saying that he wanted to marry me. He said he could not announce this marriage neither could he propose to ask my family for my hand. We had a customary marriage and we wrote a paper of it. He left me and ran away. Am I really his wife?.
Praise be to Allah.We continue to hear about such calamities. For how long will our daughters remain clueless, not realising what these criminals want?
Each one of them says: I know what I am doing and I trust this man, he is not like the others, then when he gets what he wants from her, he leaves her and runs away.
There are dozens of stories, if not hundreds or more than that, of such calamities. It happened repeatedly and it is still happening repeatedly.
Islam is wise in its prohibition of women adorning themselves and showing their beauty in front of non-mahram men.
It is wise in forbidding women to mix with men in a careless manner which leads to nothing but evil.
It is wise in forbidding women to speak to a non-mahram man for no purpose or unnecessarily.
It is wise is blocking the way to evildoers and those in whose hearts is a disease. Islam enjoins women to observe hijab and cover themselves, and to keep away from mixing with men as much as possible. It forbids a man to touch a woman who is not his mahram and forbids being alone with her, and it forbids speaking in a soft and alluring manner, and much more.
All of that is to protect her and her chastity, and to protect society in general against indecency and immorality, so that chastity, purity and modesty will prevail.
If a woman goes against all of that, she will fall prey to the wolves who do not respect the sacred things of Allah. No religious commitment or good morals prevent them from doing anything. Then the woman regrets it… but after it is too late, when regret will not bring back what has been lost.
Islam is wise in forbidding women to arrange their own marriages; rather it stipulates that her wali or guardian should be in charge of that, because he is more able than her to choose a suitable husband for her, and so that the woman will not be deceived and become the plaything of criminals.
If a woman gets married without a wali, the Messenger (blessings and peace of Allah be upon him) ruled that this is an invalid marriage. He (blessings and peace of Allah be upon him) said: “Any woman who gets married without the permission of her wali, her marriage is invalid, her marriage is invalid, her marriage is invalid.” Narrated by al-Tirmidhi (1102) and Abu Dawood (2083); classed as saheeh by al-Albaani in Irwa’ al-Ghaleel (1840).
If we add to that the condition of concealing it and not announcing it or telling the people of it, this is zina beyond any shadow of a doubt. Merely writing on a piece of paper is not enough; this paper is worthless and does not change what is haraam into something halaal.
What people call customary marriage, that is done without the knowledge of the wali, and without witnesses or announcements, is an invalid marriage; it is zina, not marriage.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
With regard to secret marriage, which they agree to conceal and for which they do not bring any witnesses, it is invalid according to all the scholars and it comes under the heading of immorality. Allah, may He be exalted, says (interpretation of the meaning): “All others are lawful, provided you seek (them in marriage) with Mahr (bridal-money given by the husband to his wife at the time of marriage) from your property, desiring chastity, not committing illegal sexual intercourse” [al-Nisa’ 4:24].
Majmoo’ al-Fataawa (33/158).
He also said:
If they get married without a wali or witnesses, and conceal the marriage, this is an invalid marriage according to the consensus of the imams. Rather the view of the scholars is that “there is no marriage without a wali” and “Any woman who gets married without the permission of her wali, her marriage is invalid, her marriage is invalid, her marriage is invalid”. Both of these phrases are narrated in al-Sunan from the Prophet (blessings and peace of Allah be upon him). More than one of the early generation said: There is no marriage except with two witnesses. This is the view of Abu Haneefah, al-Shaafa’i and Ahmad, and Maalik regarded it as obligatory to announce the marriage.
Secret marriage is akin to a relationship with a prostitute. End quote.
Majmoo’ al-Fataawa (32/102, 103)
Based on this, what occurred between you was not a legitimate marriage, and you not a wife to this man.
The ruling on customary marriage has been discussed in the answers to questions number  45513 and 45663.
In the answer to question number 7989 you will find evidence to show that marriage without a wali is invalid.
Finally, we call upon you to repent to Allah and to regret what has taken place, and to resolve not to go back to it, and to resolve to do righteous deeds and adhere to the laws of Allah, for Allah has promised acceptance and forgiveness to the one who repents from sin and does righteous deeds. Allah says (interpretation of the meaning):
“But whosoever repents after his crime and does righteous good deeds (by obeying Allah), then verily, Allah will pardon him (accept his repentance). Verily, Allah is Oft‑Forgiving, Most Merciful”
[al-Maa’idah 5:39]
“And verily, I am indeed forgiving to him who repents, believes (in My Oneness, and associates none in worship with Me) and does righteous good deeds, and then remains constant in doing them (till his death)”
[Ta-Ha 20:82]
We ask Allah to enable you to repent and to accept it from you.
And Allah knows best.