Hi. My rear shift cable goes through the chain stay. It looks like there is a plastic sleeve that goes the entire length of the tube because I was able to thread a new cable through with no problem. My derailleur shifts to smaller gears very slowly, so I was wondering, how do I replace the internal cable housing thing? Does that thing have a name? Thanks.

housing ends reamed and capped properly? rear housing loop length? the stock length will be short. what components? it would be called and internal cable guide or something similar. probably need to contact the frame manufacture. hanger alignment should also be checked and maybe a little less tension will help

Is this an older Trek frame? If so, there is no internal sleeve but a funnel at the exit end of the chainstay that guides the cable end to the hole which is why you had no problems installing it. It can't be changed.

Oh… It is indeed an old trek frame. At least I don't have to look for some obscure part now.

Sounds like some worn or damaged cable housing has too much friction going on. You can usually feel where the problem is by poking a cable through your bits of housing.

I don't think it's the housing because I just replaced it and the cable. I need to do more investigating though to make sure the cable is moving freely.

There are some crucial considerations to observe when fitting cables.

1. When cutting housing, make sure the hole hasn't been flattened, and use something sharp to ensure the crushed lining is opened up to a flare.
2. Housing ends need to be ground flat, preferably with ferrules fitted.
3. Housing length matters a lot - you need to determine the length that maximises the radius of all bends. Many bikes have a loop at the derailleur that's too short.