A picture would help ID it so we could give better feedback.

From the sound of your description, it sounds like the hardy begonia (B. grandis). If this is the case, then it will always go dormant, returning in the spring from bulbils and possibly seed. A true cane begonia (sometimes called an angel wing begonia) will never go completely dormant or die to the ground. It may drop all its leaves but with the right amount of light and water it should leaf out easily and perhaps bloom indoors.

Gosh! I thought it was angel wing - that's what the grower said it was. I'd like to send a picture, but there's nothing to photograph now [grin].

I did have some hardy begonias that seeded themselves into my yard, but the deer would get at them. Maybe they've replaced the "angelwing"

Thanks for your help!

Florrie