What is this pipe - should I be worried?
It an abandoned sewage and vent pipe. It was replaced, and the roof patched where it used to exit. Apparently they never got around to finishing the job, or just figured it wasn't any problem leaving it like it was. As to whether it's safe, since it hasn't fallen yet, it probably won't. But, you could get a ladder and pull on it to make sure. And no, there isn't a structural integrity issue. I'd finish off the basement ceiling to hide it.