I don't see any signs of rot. Is the plant firm or soft. Rotted plants feel soft. Why is it unpotted? The soil appears too dark, you should add pumice until it makes half the soil volume for better drainage .
I unpotted to see if there is any damage to the root. The bottom part of the cactus feels soft but rest is firm. Would adding pumice to the soil make it better?
Difficult to tell for sure, but that looks like root rot, the narrow, dark section below the base is indicative of this. If it is, the roots will be soft, often hollow and can easily be pulled off. Healthy roots are white, sick and dead roots are darker. Back to your question: no, if it really is rotting, the plant cannot be saved. It is too small, the rot will have spread too far. Pumice will not cure rot, I think Analogdog meant that addition of pumice will in general make a better growing medium for cacti (which I agree with, I never use peat at all). BTW, it is severely etioliated, so I guess it has grown in a spot with low light where water has even less chance of evaporating quickly enough.
