Will the headliner of my 2007 Mitsubishi 380 sedan fit through a door?

This is definitely not the sort of information car makers publish. Instinct suggests the headliner should, indeed, fit through one of the door openings, as that’s how it would be fitted on the production line. Try a front door opening first with the front seat slid all the way back and the backrest laid right down.

The other option would be to politely ask a motor trimmer how they manage this job.