Here is what happens when a leak in a flat roof is not repaired right away. When it is raining outside and the ceiling is dripping water, you just put a bucket on the floor to catch the water. When it's dry outside, the roof is not leaking, so you just forget about it! This is the ceiling in my breakfast room last October (I think???).
My grandson was up on the roof to do yearly maintenance (another coat of tar) when he stepped through the roof. The ceiling didn't actually fall in to the room until the second day of construction to extend the sloped roof over the breakfast room. All the banging of the hammers must have just been too much for the old plaster. :-) From the looks of the old wood decking, there was a leak problem before the water made it through to the room below!