My husband and I just separated and now we are stuck in a lease?

I have no job and 2 kids and now am on welfare. I was hoping my landlords would be a little more empathetic when I told them my husband and I were splitting. They are saying we are responsible for the lease till new tenants are found and will not show it till it is vacated. I am on the waiting list for low income housing for my children and I. What should I do? I can can't even put gas in my car at this point but I'm not going to stay with this abusive man just because of a lease I am stuck in. what should I do?