Oh, I just read what you added at the end after the photos. Now I'm confused. Did she repot into the same pot (without drainage)?? How long has the plant lived in the drainless pot? Did the trouble start at about the same time as the repot into this drainless pot?
I suspect this is actually a Thanksgiving Cactus but either way, the genus is Schlumbergera. They are epiphytes - in their native habitat, they attach themselves to trees or rocks (no soil). Their native environment is shady and humid.
What that means is that this plant needs fast draining, very porous growing medium and high humidity. The problem with your friend's plant is that the moisture is being held against the roots (because it can't drain) and the roots are rotting.
The only hope is to try to re-root the healthy sections. Take it out of the pot and look for some healthy roots and re-pot those in an unglazed terra cotta pot with drainage. Use a potting soil especially formulated for cactus and add a good amount of perlite (about 1/3 of the volume).
For the parts with no roots, you have two options (I would try both). For both these options, get rid of all the dried parts of the plant and just keep the branches that are pretty and green. Let any pieces with cut stem sit on the counter for a day or two to 'scab' over.
Option 1: Plant them in the same potting mix you used for the stems that had roots. Bury at least one leaf section and keep the potting medium barely damp (Not wet).
Option 2: Put the cuttings in a jar of water. Add a drop of peroxide. Keep the water clean - when you change it, add a drop of peroxide.
Keep us posted.
