Hey guys,
    What is this little tube coming out of the transmission of my 85 K100rs right under the battery shelf?

Battery breather.

So, where should that loose end be plugged into? Into the battery? My battery doesn't have a hole for it. Should I leave it loose?

A modern AGM or Gel Batterie will not need this tube.

A old acid Battery will net this tube, when it heats up it will evaporate water and a bid acid.
If the tube isn't connected or plugged with dirt, the acid will drop on the frame and destroy the frame coat.
I had that, looks ugly!

Cheers

Onya Choco, in some cases photos are the only way to go!