Does anode work if broken from tank top?

When I cleaned lime/calcium from bottom of 58 gal tank, I saw a long section of anode laying at a 45 degree angle crossways on the tank bottom with a very small "ferrous" wire still attached that was vertical up toward the top of the tank. I assume that the anode is still "grounded" to the tank body but I am not sure.

In any case, does anyone know if the anode will still work if it is not attached, that is if it is broken off and fully disconnected from the tank wall?? Do I need to try to retreive broken anode? Is there any other problem with this situation?

No it needs to be connected to the tank. The protection the anode affords is electrical in nature and the anode must be electrically connected to the tank itself.