I think runner beans are a tender perennial. If someone has a polytunnel I think you could get an early crop in the second year, well before the outside beans.
I've only ever had the roots survive once, in a very mild winter. My greenhouse started plants were already larger so I threw the old ones away.
Gosh, thanks for exccavating this thread!
Sorry to have to report that last summer's ghastly weather was good for the slugs and b***er all else here. They demolished the overwintered plants so often (despite what I thought was adequate protection) so in the end I gave in and, as another poster mentioned, dug them up and replaced with new plants. I think I had the lousiest bean crop last year that I ever had.
This spring, I was clearing a couple of bean planter sack things, and again found some overwintered roots which were viable. I decided to junk them, and now have 8 healthy looking new plants from this year's sowing. But I'm still intrigued to see if they can be grown as a semi perennial in this part of the UK, so am planning to mark the roots when I clear them at the end of the season, and pop a couple of cloches over them to see what happens. Which will probably be an easy feast for the slugs, but have nothing to lose really.
Pop a bit of copper tape around the base of the cloches, making sure there are none trapped nside - it just might help - works with pots.