Broken Hose Underneath

[AE1M]

As a few of us were traveling, someone noticed a hose hanging down under my 2016HC.  Stopping to check it out, there was no fluid dripping and not smell inside it.  This is near rear differential just forward of the rear wheel.  I just tied it up underneath so it wouldn’t interfere with the drive shaft spider to the diff.  I lowered it again for this pic.  Hose is like 1/4”.  There was no performance issue for the rest (150mi).  Anyone have an idea what this is? Tough to take pics underneath.

[richard wysong]

Rear differential breather, there should be a check valve on either the diff or the end of the hose to keep water and debris out, secure it to the underside of the body with the opening facing the rear of the truck