Gotta love it, rescue plants are a favorite (in general) of mine.
Never had great luck with "rescue people" but I have with "rescue animals".
"Rescue plants" though, sometimes free from places I work or adjacent property lines but most often from "almost thrown-away" racks at retailers. My favorite as attachment and initial cost are minimal.
Here's a fine example I potted up this morning, a "Tropicanna" canna from Lowes. I'd never seen them and broke down and paid $20 for my first even though I thought the price was ridiculous. Had to hit the nursery a month later and all were sold. Actually, many ended up on the distressed plant rack at $10. After an agreement with the dept. manager on duty to take them all, $5 per specimen. Not my best canna season so the previous occupant of this pot was exchanged for this soon-to-bloom "rescue".
This particular plant needed a little love to look as good as it does now. Five bucks? What's not to love! In 2 weeks I'll swap in a mum, get this one a well mulched spot in the garden and wait until it's time to dig and store.
Can't advise much on the begonia but best of luck!
