Air Sealing a Dropped Soffit – By protradecraft.com

Air Sealing a Dropped Soffit: Why and How in Three Minutes

When air sealing a house, begin with the biggest holes and work toward the small ones

One big hole occurs in ceilings where dropped soffits are built for ductwork, can lights, or exhaust fans.
Many dropped soffits provide a direct path between the walls and ceiling, inside and outside.

Action items for tight soffits:
Seal the section of wall that will have soffit. This can be done with drywall and caulk, plywood and adhesive, our similar.
Cover the ceiling with drywall before framing the soffit. If retrofitting, use rigid foam (or any rigid sheet stock) to cover the opening and seal the edges with canned foam.