I wish I had some pictures of some wells like that, which I repaired. In many cases the rain water gets to running down outside the casing and it makes a hole you could drive a truck into. I would stretch long boards and pipe across the hole to stand on while pulling the pump. Then I would deepen and shape the hole as best I could with a backhoe. The casing was usually large enough I could place a couple of old tires over the casing and slide them down to the bottom of the hole, which is maybe 8-10 feet deep and about that wide as well. When the tires sorta sealed the annular space I would put a small tarp or plastic over them and pour a bag or two of cement on that. After the cement hardened, I would usually pour a yard or so of cement on that and let it harden again. Then when I was sure it would hold, I would call the cement truck back and have them pour the hole full to the surface. The job usually took several days but I saved a lot of old wells that way.
The point is, if rain water can run down the outside of the casing the "hole" problem just gets worse and worse.