Ask-a-Dave's-Gardener: Why my little cactus is melting?? , 2 by Elon

Elon wrote:
Two months ago i bought two cacti and i planted them i a small wood box with some regular planting soil and small rocks (in the picture), I watered them only twice a month with not much water so they won't rot. And a week ago, after I felt before that the cactus is not stable like it don't have roots, i discovered that it really don't have roots and its bottom rot somehow. And today, after I tried (a week ago) to plant it in another small pot and watered it only ones its lower part decayed totally.
Can i save my cactus? And how can i make my other cacti avoid from same fate?
A big thanks to everyone who will try to help