I am confident that this is over-watering based on how rich and dark the soil is. That soil must just hold onto water. I'm also pretty confident the plant can be saved.
Take the whole plant out of the pot, then shake or wipe off all the dirt (or as much as you can). Dry the whole thing off with a paper towel. Then carefully cut off the soft/brown/rotted spots with some sharp scissors. Palpate the roots and make sure none are soft or mushy. If they are, cut them off, too.
On a brown paper bag, just leave the plant (or plants, if they separate) laying in the shade for at least a week. It will be VERY tempting to re-pot them but don't. After a week or so, check and see if any more leaves have browned/wilted/sunken in. If so, cut them off and repeat. If any more roots are soft, cut them off as well.
After the plant(s) has laid at least a week with its roots exposed and the whole thing is firm and dry, then you can re-pot it. But this time, the soil must be at least 50% pumice, perlite, or chicken grit. This makes it less likely to be over-watered.
Also note that some of the leaves are pale. This may be an effect of the photo because of the lighting (I can't tell). If they are not dark green, the plant needs more light.
and other members will give better advice 
