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The sender is for the fuel gauge. It "sends" the fuel gauge the fuel level reading in the tank. If the sender stuffs up, it wont make the car stall or randomly cut out, it will just stop the fuel gauge from working. The stalling/cutting out will most likely be a problem with the fuel pump itself, thats if it turns out to be a fuel related problem thats causing the stalling etc...when changing the fuel pump should you change the sender aswell?