Yellowing and getting softer are not necessarily signs of rotting. A photo of the probelm would help.

Perhaps it just isn't getting the correct type of light. You can keep it as close as you like to some bulbs, but the quality (spectrum and intensity) may be insufficient.

Perhaps in addition, it has not been watered enough, you mentioned you have not watered for some time.

Most cacti will generaly rot only if over watered or if the roots have been damaged (by insects, animals, careless humans). Sometimes a cut in the stem can start to rot if bacteria or fungus gets into it.

Waz

It is a grafted cactus  some form of epi on the bottom & a gymnocalcium on the top.
You can graft the top cactus onto some type of epiphyllum. You might try letting the bottom epi harden off & root in sand or peat  depending on the severity of the damage. These grafts are often rooted in peat but eventually need to get out of the peat. Otherwise they tend to de-graft &/or the bottom tends to rot. I have been able to get them to bloom in sand. I have also seen very mature specimens in full sun in cactus soil. This is not the greatest environment for the epi base, but the plant was probably 10 years old & plump, which is a pretty good track record for this plant.
The verigates lose their color in full sun, but the coloration tends to come back when placed in shade.