Any idea what this tool is for?
It is a Pace brand tip remover tool.
It is used to grab the hot soldering iron tip and swap it out with another one.
The black rubber is not heat-shrink... it's something that will withstand the temperature of the soldering iron tip, perhaps silicone.
If you look closely, there is also a straight-edge screwdriver at the end.  This is for loosening the tip lockscrew.
Attached is a small image of a typical Pace set-up.