Fragile paperback on cellar ceiling batts
If the room above is warm and the cellar is cold, the batts were installed upside down if the paper face is towards the cold (cellar) side. The batts mostly fall from being full of condensation (water) when in that orientation. In any case batts should have more support on a ceiling than just the backing, whether that be wooden laths or sheetrock.

Replace, possibly with some other type of insulation. If using a vapor barrier (which the paper face is) put it towards the warm side. If in a climate where warm side is hard to figure out (heat .vs. AC roughly equal), consider cellulose, which can function well without a vapor barrier.