I bought a new fuel pump for my flathead and noticed that the cup is loose and it cant really be tightened. Most of the ones I have seen are very tight. Is this important and if it fell off could it damage the engine?

 

It fits over the rod that pushes it up and down. Mine was a lottle loose too.

 

I understand that, question is if it falls off could it hose the engine?

 

Any form of material can damage the inners of an engine if it gets somewhere it shouldn't be. My buddy had to replace a piston in his dodge when a nut somehow made it's way into the cylinder and broke the top of the piston. We're all still trying to figure out how he got a nut in there
So to answer your question, yes it can possibly do damage if it fell in