All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
As for the statement that it is forbidden to use the place of Tahajjud for sleeping and that whoever sleeps there, the jinn will harm him, then it has no evidence from the Book of Allaah and the Sunnah of the Prophet and no scholar stated this as far as we know. Indeed, the Prophet said about the night prayer: "If any of you feels sleepy during the prayer, then he should sleep so that he would know what he recites.” [Al-Bukhari] Had sleeping at the place of the prayer been forbidden, the Prophet would have clarified it and he [the Prophet, sallallaahu ‘alayhi wa sallam] used to perform Tahajjud prayer where he sleeps according to the Hadeeth narrated by ‘Aa’ishah and by other Companions .
As regards performing the night prayer without interruption, then this is very desirable and it is disliked to stop praying at night, as the Prophet said: "The most beloved actions to Allaah, are those done regularly even if they are small.” [Muslim] Moreover, the Prophet said to ‘Abdullaah Ibn ‘Amr : "O ‘Abdullaah! Do not be like so and so who used to perform the night prayer and then he stopped praying it.” [Al-Bukhari and Muslim] Ibn Hajar said: “This Hadeeth proves that it is desirable to keep doing the good deeds that a person used to do without being negligent about them, and we deduce from it the dislikeability of interrupting an act of worship even if it is not an obligatory one.” For more benefit, please refer to Fatwa 81337.
As regards the statement that the jinn pray behind a person who stands in prayer at night, then we are not aware of any Sharee’ah-based evidence that confirms or denies it.
Therefore, we advise your mother to continue the night prayer and not abandon doing so because of the reason that you mentioned in the question. If she sleeps during some nights and does not stand in prayer (at night), she is not sinful because the night prayer is desirable and not an obligation.
Allaah Knows best.