Yes. You must continue to pay rent as long as the landlord owns the house. When the landlord looses the foreclosure proceeding in court, you no longer have to pay the landlord rent. But foreclosure proceedings take a very long time, and often end with the landlord simply modifying their mortgage and keeping the house. So just because a landlord gets served with foreclosure papers does not mean you no longer have to pay them rent. The landlord can still evict you for nonpayment of rent even when the house is being foreclosed on.