While I was putting in anchors to hold a shelf standard I had one that didn't install right and I was left with a one-inch hole. Some kind of anchor or support absolutely has to go there. It's too small for me to go inserting a piece of lumber behind it (not a good place for it either) and I can't find an anchor that would hold to a hole that size.
There is a butterfly anchor sold at most hardware/home stores. It's a V shape with a nut and a spring at the point of the V. It will fit into a 1" hole and then expand once pushed through the hole to a wider diameter. You may need to drill the diameter of the hole in the standard out to accommodate the larger screw. But these are very strong drywall anchors.
There's a couple of ways to play this. It depends on how much work you want to do
- There's a wide variety of drywall anchors on the market beyond the toggle bolt. My suggestion is head to the big box store and buy the largest toggle-type you can get. The best solution here is what one calls a "driller toggle", where a large metal plate drills in, and then the screw forces that metal plate vertical. You might want to repair the drywall first, just so it can't wiggle.
- Widen your hole (as in cut a larger opening) and put a 1 x 3 or 1 x 4 behind the hole. Let's say you cut a 4 inch square hole. Cut your board to 6". Take some drywall screws and screw it to the drywall on either side of the hole. Put your cut section back in, screw it to the board as well, then tape and mud it. Once your wall repair is complete you can screw the shelf through the drywall and into to the board directly.