You have the obligation to pay the landlord rent as long as the landlord is the owner of the property. This oblication does not change because you receive a summons in a foreclosure action. Depending on the provisions of your lease, you may be able to terminate your lease early because of the foreclosure action. You should consult an experience real estate attorney to review your lease and advise you of your options.
Short Answer: No
Long Answer: A renter may not legally stop paying rent or terminate the lease if a foreclosure summons has been served. If you are the landlord let me suggest that you (1) hire a foreclosure defense attorney so that you will delay foreclosure sale for a substantial period of time and until after the expiration of the lease. If the bank's case is weak you might be able to obtain concessions on loan balance and interest rate that allow you to keep the property. You also need to have a frank discussion with the tenant about the issue. If the poster of this question is the tenant you should call your landlord and discuss the issue. You can't ignore the 800 lb gorilla in the room. Your landlord should not ignore the foreclosure and its in the tenant's best interest that the landlord be pro-active, avoid a default (the fastest way to lose a foreclosure case) and fight the foreclosure. For additional information for homeowners in foreclosure, including firm's rates please see out blog.