This is my rear shifter cable housing at the front of the down tube. As for shifting, I lost the two highest gears but otherwise it works okay.

New length of 4mm index outer housing in Gray (or if there's enough, remove the inner wire and cleanly cut the offending stub off, and install a new 4mm plastic ferrule). Inspect the inner wire and if it's damaged, replace it as well.
Inspect the adjusting barrel and spring; replace if necessary.

Alan

Realy all that needs to be repalceed is the cable housing and maybe the cable. If the cable is good there is a very good chance you can just cut the cable housing just above the brake as said above.

I would change the cable adjuster, cable and housing.

"Why is their an adjuster there?" <--- some bikes have cable adjuster there, other ones doesnt, there is no rule about where u put them, in a matter of fact you can ran the bike w/o able adjusters because the RD has a cable adjuster already (at least campagnolo ones) and the FD pretty much doesnt need one at all. The other detail... like 95% of the cycling population has no idea what are those things for"

i would wonder how it got that way.

it's possible that the housing was too short to begin with and wasn't being supported properly at the adjuster end. just a guess...

Was the frame possibly designed for drop bars? My Salsa Fargo frame came stock with adjusters in that position -- one on each side of the upper downtube cable stop.

It's compressionless (derailer) cable housing. Brake cable housing's different. Probably just normal use.

I want some there so I can tweak adjustment while riding after switching wheels.

Most road bike shifters do not have built in adjusters; if one wishes to adjust their derailleur on the fly, it is either placed in the downtube stop or what is becoming more common, in-line.

You can add one back by the RD itself, too, inline, you can see what it does
on the repair stand, better, with the one close at hand..

"install a new 4mm plastic ferrule" A brass ferrule might not break like the plastic one did.

There's two barrel adjusters along the one cable (downtube and at the derailleur), not too sure why but that's how it came.

With the smaller diameter (4mm) index housing used on the current crop of Shimano components, they require the corresponding plastic end ferrules.

Standard brass ferrules are made in 5mm only; they're too big to fit properly over the smaller diameter housing.

The adjusters on the downtuble are found on touring bikes . It makes it easier to adjust on the fly with full loaded bike .

The adjusters can be found on all kinds of bike. I have a touring bike , a commuter bike (really a cyclocross bike) and a go fast road bike with them.

degnaw: You'll need to trim the end of the cable housing at the very least. You can get metal ferrules in 4mm from Bike Tools Etc. If you want colored ferrules, Origin 8 and Jagwire carry them too.