You have 2 choices, you can either prop it up and figure out how to re-secure it or remove it so it doesn't fall. You can then see how it was put up and put it back. If it's damaged, get another piece and put it up.
Yep, you'll need to add fasteners to re-secure it or tear it out and replace it. Then scrape tape and mud, re-spray (unless you decide to do away with the texture). Tearing it out might be the best bet so you can actually see why the piece is coming loose....
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