I woke up this morning to find a random hose hanging from my xj. The hose starts at the spot I've got circled in the picture and has a small white plastic cap on it. I have no idea what this thing could be and I haven't been able to find the same part on any other photos of xjs.

I got a somewhat shoddy pic of the disconnected end of the hose as well. It's got a bit of protective wrapping on it but I wasn't able to find a workable entry point for it into anything that I could get to without stands.

Does anybody know what this is?

I'll get some better pictures in the next couple of days.

 

I can't see anything from those pictures but based on your description it's most likely your differential breather.

It's there to provide a vent to atmosphere for the diff, but it needs to be raised up higher so water and stuff doesn't get into the diff.

 

Would there be any other breathers on the front end?

 

No. Put it back up near the brake booster and plastic tie it in place.