I don't know the exact species of this cactus, but it does look very similar to me to some I have seen which grow prostrate (also known as creeping). I imagine this is its natural growth pattern; someone else may be able to identify the species and verify this for sure. If that's the case, you have nothing to worry about. Here is a photo of some cacti with a creeping growth orientation:

Your soil looks way too dark, rich and water retentive. AND the cactus need more light. That is why it is stretching out. If it is soft, it does sound like rot. You need to up root it and see what is up wittth the roots and see it they are rotted. Then you need to cut all the soft and discolored stuff off . Take a some alcohol and wipe of the knife each time you cut to kill bacteria. Then sprinkle your cut on the cactus with cinnamon (a great natural fungicide) and then let the cactus wounds callus for a week or so. What do you have your cactus planted in? You need to get a very fast draining mix . Take that mix and dillut it 1 part your soil with 3 parts inorganic grit. It could be pumice, turface, perlite, or a combination . Google Al's gritty mix. Growing cactus is all about the soil. NOW, how much are you watering? Once you put your cactus in the NEW soil, DO NOT water it till you see roots. Then start very judiciously a little bit at a time . You can mist. Cactus take in moisture through there roots not their stems. They can collect moisture on their needles so a bit of misting is ok. But be judicious and let things dry out well.

I have the same cactus and the same thing happened... I put the broken off piece in a dry place for a week or so, then replanted it in a pot and watered it weekly for a month. Lots of roots grew back. The remaining nub stayed where it was and has grown two new heads. Both parts are now thriving in the ground. HTH

That's the way they grow. They sprawl along the ground as they grow, not as a columnar plant.