Short answer: yes. Long answer: Maybe.
He/She still owns it and have legal title to the house, so there's really nothing you or the new tenant can say about it. However, the landlord may not own the home for the entirety of the next lease if the foreclosure sale happens while the current tenant occupies the property. The buyer (bank) at the judicial sale may honor the lease, or they may argue that it's invalid, especially if the rent is below market rate. That said, if an investor purchases the property and the rent is market rate, they may be thrilled to have a turn-key property that instantly generates income.
Note: I am not an attorney and this does not constitute legal advice.