Ok, so I took it out of the pot and cleaned the roots.
Coincidentally, today was watering day. The soil was bone dry, to the core, so it couldn't have been due to overwatering.
It seems to bee all the same plant, at least I am 100% sure that too of them are.
However, I found no signs of rot. No rotten roots, no stump where the dead pup used to be, no more goo, and no signs of rot on the other offshoots... I'll take it as a good sign for now, but it is kinda weird, it looks almost like the rotten pup was not connected to anything (wich the last time I reported it, I'm pretty sure it was...)
I guess I will wait for about a week to let the roots dry and heal, and then pot it again in clean soil, and hope for the best.