Running close to empty will ruin fuel pump?

Just a slight correction here. Most fuel systems (being made now) are now return-less systems, so there is no constant circulation.
I do agree that fuel pumps don’t overheat or fail due to low fuel levels. I do know that they can fail due to no fuel conditions. I have seen older pumps that couldn’t handle the stress when run dry. I have also seen the fuel pump fuse blown when someone ran out of gas. Of course, there are many more examples where running dry did not cause any failure.