Fixing hole in ceiling for recessed light after water damage
There are two issues: support and cosmetics.

For the support, you could remove the can, insert thin, long pieces of wood (something like a paint stirrer) in the space above the lip of the can, overlapping the newly opened area. I would put in two strips, opposite each other. 

I would hold them in place by putting screws  upward through the solid area of drywall, one on each end. This should give more body to hold the can in place after filling the gaps.

For cosmetics (and some support around the new strips) I would use a hardening spackle (not taping compound or a lightweight filler) to fill below these new strips and build up the edge around the hole. Then, after drying, sand the whole thing smooth before inserting the can.