I have say 1/4 inch soft rubber hose hanging from the rear end of my explorer. Someone hooked it back up at one time and has come off again and I can't locate where it goes so I can hook it back on and clamp it.
Rear End on 1999 Ford Explorer
Sounds like it's just a breather hose to vent the axle to the outside air. Keeps pressure in the axle housing from building up and pushing gear oil where it shouldn't go, You can wire tie it up high somewhere but don't kink it as it needs to breathe.