Can I apply for temporary residence

I left my employer as they promised me a job but there was no job. I didn't even stay for 3 weeks but I know they had started the process of getting residency and foreign expert certificate for me as they took me to get a health examination. They have all the results. I do not have anything except my passport. Since I resigned so early they refused to give me a release letter saying that I hadn't worked I won't need one. They also mentioned they cancelled all applications for me so is it ok if I apply for myself? Can I go to the police and ask for temporary residency and then have a new school get me invitations etc