I think you will find that there will be more than one option out there for you if you have to move.
They should be able to help find you a place where you can live where you can take your kitty

I'm so sorry this is happening to you, BF. But I'm glad that you can advocate for yourself, and you have the support of your case manager to help you through this. If she runs into problems, I'm sure she has her own support system in her office that will help her help you. You will not be thrown to the wolves