Are they the tuber type or the fiber root type? The tuber type you let die back and put it away for a yr. The fiber type, we have about 5 types, we bring inside before frost. You can prune them to your heart's content, and put the prune cuttings in water to root, and you will have more. I have 5 "huge" outside ones, from our cuttings. I have seen plants smaller than ours selling for $50. Good way to get plants for exchange also. Angel wing type love to be pruned, I sort of give up on the other type. I don't have any rex type anymore, they were too hard to do.
Darlene

The tuber type, when you go to anyplace that sells bulbs in spring, look there. They will have begonia tubers for sale, so you know what they look like. If you dig it up, it will have a nice tuber (like a small brown potatoe) on the bottom of the green plant. If it is a fiberous begonia, then the roots are fiber roots, like hair roots. I see that you live in Ca. and that is why the plant survived. Here they would freeze, and not come back, tuber or fiber type. Here we take cuttings of the fiber type, and the tubers, we dig & store in a cool place for winter.
Darlene