Are they like Armstrong ceiling tiles, 12" x 12"? These have a tongue & groove system. I think you could just pull them off up to the area where they are sagging and replace, but it would be nearly impossible to only fill the middle, as they fit into each other you have to go all the way to a wall.

Ours were sagging from a water leak so I replaced the whole ceiling. It wasn't very expensive, just somewhat tedious work for one person. If these are the type of tiles you the advice is treat them gently as they damage very easily, use a good staple gun and paintable caulk to fill the slender cracks before priming and painting.

I have seen some houses where the 12x12" tiles are sagging. Each tile is SUPPOSED to be stapled or nailed into something, but sometimes the builders didn't do that. Sometimes they were just glued and over 50 years the glue fails. So over time the tiles will sag. Heat might cause them to expand and sag, but moisture is more likely the culprit.

If you get new tiles, be sure there is something to glue and staple the new tiles to. If not, put 1/4" plywood all over the ceiling and staple and glue the tiles to those. I'm still referring to 12x12" tiles. Hanging ceiling tiles (18x36"?) are different.

We have an old tongue and groove ceiling that is still tight but needs help - old and faded/yellowing. How can this be painted or made to look fresh again?