What's this strap on the hammer for? (piano repair)

[fiasco]

Was repairing a broken hammer on my piano yesterday (had to glue the stick together that connects the hammer to the base) and when I was done and let it dry the hammer wouldn't fall back down into position after it hit the strings (this is the G below middle C).  So I'm trying to figure out why it's stuck in the "up" position, and I noticed that the little strap which runs from the hammer base to  the, I don't know, the lever part right under the keys (I've never repaired a piano before) was ripped.  I thought that this was the reason why the hammer was staying up, so I was trying to figure out how to repair it (it's so hard to get to these things amongst the lattice work of wood and wires) when I noticed that there's a little wire that sits under to base of the hammer that acts to push the hammer back into position after it hits the strings...  This was out of place, as was a few others I noticed while in there.  So I pushed it back and now the G works fine, Elmer's Glue and all.  However, that strap thing is still ripped and disconnected.  They seem, on the other keys, to be too slack to really be doing anything, but it looks like someone went through a lot of trouble to put them there, and I know they're there on all pianos, but can't figure out why.  This strap is now ripped on my G, but you whould never know it.  So, what is this little strap for, and should I bother trying to fix it?

[berrt]

It has a function only when you remove the action (prevents dropping of the hammers).