I'm afraid it is bad news, I've never had anything recover from soft, brown looking parts. What you might do is cut a piece above the rot if one still looks firm and normal, and propagate it. They can rot so easily,you may not recognizeit starting.If they are well watered but you have some unusual cold or rainy days, you should watch for problems. It is better to lift/or touch the soil to see if the plant really needs water, if it looks okay wait another day to water, it won't collapse overnight.Believe me, I've lost my share. There is a chance it may grow again from the soil level or just below, depends on how bad the rot is and there's no way to tell, just watch and see (cross your fingers).

Thanks for your reply and your vote of confidence! So you think they will be okay, but go dormant at a later date. I will taper off the water to help them get the idea. Maybe I should put the boliviensis in the three season room, which is cooler. The boliviensis is in a tippy pot that was hanging, but now is perched on a table, and it got off balance and landed on the floor. It lost a stem, but seems okay. I have to get some hooks installed, or something. I hate moving. If the white one goes dormant and doesn't come back, I have one cutting that I didn't give away that is just beginning to bloom, so maybe I will have tuberhybrida begonias still. What a funny name! Like a turbo-begonia. I do okay with plants that are okay with getting dry in between watering. I kind of have one style of plant care, and it seems to work for a lot of things. I try to look at the plant and see what I think it needs. The four kinds of begonia that I have seem to be okay with what I do. They seem to be generous plants. I also have a beefsteak begonia and some other kind of angel wing type that I'm not sure what it is, but a woman traded me a cutting of it for a cutting of the beefsteak one. I think it maybe is a fibrous rooted one. I bet there are a few kinds that I'd better not try, though. Anything that likes to be wet and humid and warm I'll kill. I am happy to have a forum for just about any plant that I want to learn about. I really appreciate the people who answer my posts with their more extensive experience. Thanks again.

Also it depends on the begonia that you have rooted if it is a dragonwing for example just keep them growing and pot them up in a larger pot or plant them in the garden this spring you will have much larger plants. If they get too large or leggy then prune them back and you can root those cutting if you desire. If they are dragonwing here are two tidbits that I picked up that maybe helpful: 1 If the cuttings that you rooted does not have a bud union at the leaf node where you rooted it, it will not spread ( no basal growth) only grow as one long branch. 2 When a dragonwing is pruned most of the new spreading growth comes from growth at or beneath the soil level which is related to the bud union from tidbit No.1. I am no expert by any means

There are many forms of 'du' each with its own name. (Voo Du, Deja vu, Danadu, etc) Xanadu tends to have a little wider leaves. I am trying to visualize by the size of pot you gave. This could be a type, it's possible that these are semi-juvenile leaves but an 8 in pot is much too large for the plant to still be throwing out juvenile leaves unless it is extremely stressed. Try putting it about a foot away from a south facing window and see if that helps its leaves broaden. This will also help to prevent Chlorosis. Philodendrons are notorious for this if they do not get enough light. The more leaves it has, the healthier it will be also. (Also keep in mind I just moved from California where Xanadu is a landscape plant and grow to be about 10 or so ft high without support. The leaves can get huge.) You can also try upping the humidity in lieu of watering too often. Putting the plant next to other plants or misting it with a spray bottle daily will help.All of your plants will benefit from frequent misting, especially during the winter where it tends to be dryer inside. In about 2 months or so, depending upon where you are, you can start misting with a very dilute amount of an all purpose fertilizer (Eleanors VF-11 is a wonderful all purpose that does wonders for all sorts of epiphytes) can help it come back. (dilute meaning 1/4 strength or less) As for orchid bark. I would get the large because Philos' roots can be pretty clingy, they like to anchor in the bark, smaller bark will break down too quickly. You also want to make sure your mix is well draining and the plant never sits in water. HTH