They can fade in a number of ways, particular stocks tend to have particular issues.

The 'red' prints you see are usually a result of the Cyan and Yellow dyes in the film fading away, leaving just the magenta layer, which is why they look 'pink', that layer is the only one left with any information in it.

Sometimes all layers fade leading to a brown looking print (easier to restore) and other times the magenta layer fades out leaving you with a greenish looking print.

So the prints don't usually 'become a different colour' as such, i.e. the cyan layer doesn't drift towards being orange or anything like that. It is usually one or more dye layers fading which changes the look of the film as the other dye layers have more information in them (have faded less) than the ones that have faded. So when you get a very Magenta looking print, the other colour information has often completely faded away, making restoration close to impossible (i.e. you have to find other potentially lower quality sources for the other colour layers)

The imbibition process leads to very stable dyes, so typically an IB print will have very little fade.