When the East Coast monsoons move off to Atlantic regions unknown, wait for the ground to dry just a little. Then take a shovel and carefully excavate the area. The only way you can assess the possibility of repair is to understand why the ground gave way in the first place. It may simply be that the backfill or natural subgrade in the area gave way around a subterranian boulder or other object due to the rains. The compaction below the ground may not have been sufficient over time to keep it in place when exposed to torrential rains.

Another possibility, and one of concern, is that a manmade structure below grade, like a septic tank, leaching tank, or cesspool may have given some due to the rains. If there's a possibility that such a structure is underground there, taking care when digging would be advised so as to not suddenly come upon a sizable hole beneath your feet. If to your knowledge there is nothing like that in that area, no old oil tanks or what is described above, then it may simply be a small local settlement. I don't think Long Island is known for its underground caverns...but one never knows.

[This message has been edited by treebeard (edited May 30, 2003).]