I think you could use 'shed' for small amounts of ceiling plaster dust coming down. "The person in the room above was jumping up and down, causing the ceiling plaster in the room below to (fracture/break up/fragment/crack/...) and (shed/give off/emit/...) dust into the room."

"The person in the room above was jumping up and down, causing the ceiling plaster in the room below to shed dust into the room."


(I added a little of qualification to the pour section above also.)