Well, my luck has run out.
Exhibit A: my back yard patio.
See that mess over on the left? That's where one of the patio stones fell through into a gigantic hole.
Here you can see better the situation. I called the city, who did a dye test, and confirmed that there is a break either in the sewer lateral or the storm drain.
Unfortunately, the hole is quite deep, and extends under the raised area, not under the lower area. I think the Arbor vitae is going to have to be retrieved; the nearby grass can go: it'll regrow itself.
This evening I tried to remove some of the dirt above, and the decorative rocks that I don't want to lose into the abyss. However, I also didn't want a bigger hole than I had to if it was going to rain again, and it seemed quite likely that it could cave in and then where would I be? I felt like it would be easy for me to make a bigger mess instead of a smaller mess. In the picture above, you can see one of the bricks is a little raised; I was about to retrieve it when I realized that the only thing holding the two bricks on either side was the tension between the three. If I pull out the middle one, the other two will fall, and the hole extends a bit behind that, too, maybe a foot or two, so all that dirt you see behind it would probably also fall.