What is this?

[Chitownjohnny]

Ok I was working under my 2006 liberty today and noticed a rubber hose hanging down, I followed it up and it went to a block on the top of the differential on the driverside that appears to have brake lines coming off it.
The hose has a metal clip on the end that appears to allow it to clip onto somewhere underneath.

I recently had to have the fuel pump replaced (by a dealer) and I assume it was knocked loose or forgotten.

In the pic in is the rubber hose running straight up and down. Blue arrow pointing to it.

Any help on what it is or where it goes would be great

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[Gyro]

Rear diff breather hose.
zip tie it somewhere high but leave enough slack for flex.

Gyro

 

[CzarKJ]

Typically we put it up ontop/next to the gas tank if it is long enough.

 

[04Liberty]

There should be a clip on the end to attach it to the underbody. That may have rusted out/failed, hence why it's hanging.