Legal Question in Landlord & Tenant Law in California

Not if the deed of trust that was foreclosed on was in place when you signed the lease. In that case the deed of trust has priority over the lease and any other interests in the property created after the deed of trust. As a result, all rights created after the deed of trust are wiped out by the foreclosure.

If the lease pre-dates the deed of trust then it is more complicated unless the lease was recorded (rare). In the case of an unrecorded lease that pre-dates the deed of trust, the question becomes whether the lender had actual or constructive knowledge of the lease. Whether that is the case or not depends on facts and circumstances that would be too complicated and detailed to go into here.