How should he pray if he can't find anything to wear except a garment on which there is some impurity (najaasah)?
Question

                If my garment becomes impure and I do not have anything else with me in which I can pray, how should I pray?.
Praise be to Allah.
    Firstly: 

    Prayer is not valid if offered in an impure garment, if the 
    worshipper is able to pray in a clean garment, because Allaah says 
    (interpretation of the meaning): “And purify your garments!” 
    [al-Mudaththir 74:4]. 

    And because a woman came to the Prophet (blessings and peace 
    of Allaah be upon him) and said: Menstrual blood may get onto the clothes of 
    any one of us; what should she do with it? He said: “She should scratch it, 
    then rub it with water, then wash it, then pray in it.” Narrated by 
    al-Bukhaari (227) and Muslim (291). So the Prophet (blessings and peace of 
    Allaah be upon him) commanded her to purify the garment of menstrual blood 
    before praying in it. 

    Secondly: 

    If the garment becomes impure and he does not have any other 
    garment in which to pray, one of the three following scenarios must apply: 

    1.He is able to wash the spot 
    where the impurity is on the garment and pray in it, such as if the impurity 
    is in a spot on the sleeve, for example. So he has to wash it and pray in 
    the garment, because he is able to pray in a clean garment and he has no 
    excuse for praying with the impurity there.

    2.He can take off the garment 
    without uncovering his ‘awrah, such as if he is wearing another garment 
    under it that covers his ‘awrah. So he has to take off the garment and pray 
    in the clean garment. Hence the Prophet (blessings and peace of Allaah be 
    upon him) took off his shoe whilst he was praying, because Jibreel came to 
    him and told him that there was some dirt on it. Narrated by Abu Dawood 
    (650) and classed as saheeh by al-Albaani in Saheeh Abi Dawood.

    3.There is no other clean garment 
    in which he can pray, and it is not possible to wash the spot where the 
    impurity is on the garment. The correct scholarly view is that he should 
    pray in the impure garment, and he is excused and his prayer is valid, and 
    he does not have to repeat the prayer after that.

    Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) 
    said: 

    What if a person cannot find anything but an impure garment? 
    It was said he should pray naked, or he should pray wearing it and repeat 
    the prayer, or he should pray in it and not repeat the prayer, and this 
    is the most correct of the scholarly views, because Allaah did not 
    command His slave to offer the obligatory prayer twice, unless he did not do 
    the obligatory action that he was able to do the first time, such as if he 
    prays without taking his time; then he has to repeat the prayer, as the 
    Prophet (blessings and peace of Allaah be upon him) ordered the man who 
    prayed without taking his time to repeat the prayer, and he said, “Go back 
    and pray, for you have not prayed.” Similarly, if a person forgets to purify 
    himself and prays without wudoo’, he has to repeat the prayer, as the 
    Prophet (blessings and peace of Allaah be upon him) commanded the man who 
    did wudoo’ and forgot a spot on his foot which the water did not touch to 
    repeat his wudoo’ and his prayer. As for the one who did what he was 
    commanded to, to the best of his ability, Allaah says (interpretation of the 
    meaning): “So keep your duty to Allaah and fear Him as much as you 
    can”[al-Taghaabun 64:16], and the Prophet (blessings and peace of Allaah 
    be upon him) said: “ If I command you to do something, do as much of it as 
    you can.” End quote. 

    Majmoo’ al-Fataawa, 22/34, 35 

    And Allaah knows best.