The washing instructions on most rubber-backed area rugs read, "Machine Wash Warm. Do Not Tumble Dry," or something to that effect. I consider these directions suggestions, as I machine dry my rubber-backed area rugs within an inch of their lives. The effect? Holes in the rubber. And sometimes, if I’m really lucky, rubber confetti sifting to the floor as I take my toasty rug from the drier.
A few years ago, after growing weary of spending the cash to replace perfectly good rugs with holey backs, I tried repairing them with caulk, although I had no idea, at the time, if caulk was machine wash and dry-able. It is.
Pick the loose edges of rubber from your hole.
Spread a generous layer of caulk–any kind or color will do–over the hole plus about a half inch beyond.
Let the caulk dry completely, for obvious reasons, before using the rug.
After a half a dozen trips through the washer and drier, the caulk might loosen a bit. Just yank it off and perform another patch job.