Help! How do I remove a stubborn broken screw from my wall

One of the former owners of our house left a screw in the wall — the head is broken off the screw and I have tried everything I could find online, but nothing has worked so far.

Our walls are plaster, but this particular part of the wall is extremely solid, maybe like concrete or something? I nearly stripped a couple screws just trying to remove a wall-mounted coat rack that the last owner also left behind… (now I know why… because it was hiding the broken screw)

So far I’ve tried using pliers, even wrapping rubber bands and/or duct tape around the screw to give it better grip. All it did was rip up the rubber bands and duct tape and nearly stripped my pliers. I’ve also tried drilling holes around the screw to loosen it, and broke a drill bit that is now also stuck in the wall. 😭 It literally hasn’t budged at all.

Any suggestions?