I tend to put most of the scraps that are not suitable for chickens in my worm bins, when its completely worm castings (and worms) I dump it in one of the Chicken runs for them to scratch through. Its not just full of worms but other insects and all those nasty things that chickens shouldn't...
As far as breeds that would be better at surviving without milled feed I would go with older breeds, breeds closer to their wild roots and bantams. I personally like the idea of bantams for this not that I plan on every having chickens that must forage to survive but its good to be prepared...
My cousin only feeds table scraps, scratch grains (occasionally) and lets them free range a cow pasture. They lay just fine but he has more than 1 acre per bird with plenty of cow Patties to attract bugs even in winter They also eat all the seeds that fall out of cows hay and access to...