I can see myself living in my car soon.

I have been renting this unit for 2 years now and they have just found out I have a dog. They have sent me an eviction notice already and I have told them the dog will be gone soon. I am lying. He is my best friend and I can't get rid of him. I love him.
The problem is I can't find anywhere to move to. It seems nobody wants pets in their rental properties anymore. Can I just squat here and say I am not going until I find somewhere else to live or can they just kick me out in the street?