That's a pretty common way they do stuff like that around here, too. They do mark off stuff that's being worked on on road surfaces, but stuff on sidewalks/etc rarely gets any kind of warning or marker unless it's the city itself doing the work (rare). Usually it's some sbu-sub-subcontractor, and most often the workers don't speak any English, and have had no training in what they are doing, either, so it's no surprise that it's also not marked off (usually their trucks don't even have any warning markers or other markings on them, just whatever they usually drive around, I think).
I've never ridden or walked into it, but the surfaces of many repaired sections bear squished witness to those that did.
What I *have* ridden over and nearly been killed by a couple of times are the places on concrete bike paths or sidewalks where they have pried up a couple of large squares of it (all the way to the break lines), done work, then just set them back down. They're not pushed all the way back down into the same level at the center, but rather left up in the center as if they were "ramps". Half the time both pieces are left with their center ends pushing on each other end-ways so they make a double-ramp. The other half, the dangerous one, is when they put one piece down level and the other piece resting on top of the end of the other, creating up to an 8-inch "cliff" on the other end of the "ramp" (depending on thickness of concrete plus whatever dirt they didn't pack down properly under it).
That cliff is invisible while you're riding up to it from the ramp end in most cases, as there is often dappled shade on it from trees or bushes, so you don't really see that it's a ramp until you feel the incline--it's way too late by then as the front wheel is about to get slammed onto the ground on the other end, down whatever distance the cliff is.
If you're going fast enough you'll launch into the air a bit, but my CrazyBike2 is heavy enough that it can't really do that at speeds I'd be going on concrete paths (hate the bumpbumpbumpbump of the edges at faster speeds; I don't mind random ones as much as repetitious ones).
So while that's not the worst thing I ever ran over, I guess it's up there.
And chinaberries are up there with marbles and sun-dried olives for something you don't want to ride over with a normal-weight bike on pavement.