If a residential property in New Jersey is foreclosed, does the creditor under NJ law have the right to collect for deficiency?

Unfortunately, unless you have received a notice from the creditor, you may still be obliged to pay rent to the current property owner. If so, make sure you pay by check or money order or receive receipts because you may need to prove to the creditor at some point if they seek to evict you for non-payment that you made payments for the rent to the landlord and that any non-payment of the mortgage was the landlord's fault not yours. If there is any contact from the lender to you make sure to contact any managing agent or attorney to arrange where and how payments should be made.