Methods and systems are provided for controlling a vehicle fuel pump at a fuel shut-off event based at least in part on whether combustion stability issues, or potential stall conditions, are indicated in a drive cycle prior to the fuel shut-off event. In one example, a method may include maintaining power to the fuel pump responsive to the potential stall condition being indicated, and independent of an indicated pressure in a fuel rail configured to receive pressurized fuel from the fuel pump, and where the fuel shut-off event includes a deceleration fuel shut-off event or an idle stop event. In this way, fuel may be kept flowing across the fuel pump during fuel shut-off events, responsive to indications of combustion stability issues, such that fuel pump cavitation and other engine and fuel pump-related complications may be avoided.