Well, I don't know about eels staying on the bottom, i often see them cruizing all levels.
It is very common for newly introduced eels, to swim around the top of the tank, sticking its head out of the water.
Eels are mater escape artists are will find the smallest hole to get out.
It is very common for them to nd up on the floor, in an overflow, or in the sump.
You may be able to keep one, but i would rig up some sort of screen that would prevent them from getting into the overflow box.
A tight fitting lid is a must, may even need to be weighted down, depending on the size of the eel.