I agree that more information would be nice. I will assume you are referring to centrifugal pumps. In the parallel configuration you describe, each pump should have a check valve on the discharge so that it won't spin in reverse if it trips off. If the check valve works correctly, when a pump shuts down, it will only see suction pressure. If there is no check valve, it will spin backwards. It could suffer damage if allowed to spin in reverse at full speed (or faster). If the check valve were placed on the suction side of the pump (not recommended) it would pressure up to full discharge pressure from the running pump. For an API pump, this would not normally be a problem since the suction flange and the piping up to the valve should be designed for that pressure. You need to get the maximum allowable working pressure for your pump and use the P&ID to verify what pressure it will see under various conditions (running, tripped, etc) and verify that it will not see any pressure which it is not designed to accommodate.
Johnny Pellin