You have wallpaper over an old plaster ceiling that is cracking. You can roll a coat of ceiling white on it and it might be fine, or the moisture in the paint could cause the paper to start peeling. That crack looks pretty nasty so could fall on your tenant any time, or might never be a problem. The easiest solution is to add a layer of drywall which makes it smooth and holds the plaster in place, but obviously that costs more money.

My first apartment had an old plaster ceiling. It did indeed fall, directly on the bed. Fortunately for me, I was not in the bed. Unfortunately for the landlord, my father dealt him afterwards.

Thanks, Hallet & Co! Unfortunately, I'm the tenant, and if I want it repaired I probably need to do it myself. I'm decently handy, do you think I could realistically cut out the problem areas, fill with drywall/mud/prime and paint? Or would a DIY job inevitably just make it worse?

Don’t touch it. Roll a coat of paint on it and hope for the best.

got it, I won't – appreciate the advice!