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.
What is mentioned in the question is a trick against the government to provide you with housing because you agreed with the agency that rents the house to you to sue you in court in order to evict you from the house so that you would get a temporary housing and then a permanent housing because of being evicted through this unreal displacement, as we understand from the question.
Therefore, it is not permissible for you to do that because it is fraud and deceit to obtain from the government that it provides you with housing while you do not fulfill the conditions of being entitled to it.
If you are in need of government housing, then you should undertake the legitimate means in order to get it.
Allaah knows best.