Who has the right to stay in the house after break up?

I’m writing in desperation. I moved here years ago for my Dutch partner. I worked here and made my life. Last year we got the house because of my high incomes in last and because of my partners long time on waiting list. I got sick (unfortunately long term and I needed to quit my job) and right now I’m receiving WiA-uitkering from UWV. We broke up with my partner and now he wants that I leave the house. We both are equal in contract. As I’m living around social minimum I kindly asked him to leave, but he doesn’t want to. I can’t leave because I can’t afford but he made pretty high incomes last year that would be enough for him to find a new place. He is willing to start the law case but I can’t afford this. I have nowhere to go but I have the same rights to stay in the house. Could you please advise what to do in this situation?