my 2008 f150 5.4 fuel pump stays running even with engine off & key out of ignition what is causing this

Are you absolutely sure it's the fuel pump? Or are you assuming it is the pump because that sounds dangerous .. not to mention how hot a 'runaway fuel pump wire can get. If someone installed something wrong they could be "back-feeding" the run circuit. (seen it happen on a new sound system) If you shut the key off the complete "run" bus inside your fuse box is remaining energized ... if that happens the engine should still run even if the key is removed.

Yes the fuel pump staying on when the key is out running the battery down what is the problem