Legal Question in Landlord & Tenant Law in California

No they do not have that right. As long as you own the property you have a right to the rents. You need to be careful, however, because a foreclosure may put you in breach of the lease or rental agreement. So you need to do everything you can to postpone a foreclosure to past the end of any lease term, or if you are on a month-to-month rental, and a foreclosure cannot be avoided, that you give the tenants 30-days notice of the foreclosure (60-days if they have been there more than a year). It is best to deal openly and honestly with your tenants about this, both their obligations and yours and give them assurance that you will live up to yours, but expect them to live up to theirs. If you are trying to keep the house, make sure they know that, and that you will honor the lease or rental agreement. If you are going to let it go eventually, work with them so they don't get disrupted any more than possible. If they still won't pay rent, you'll have to evict them.