In Fire Emblem Fates, you can choose between Classic, Casual, and Phoenix game modes. In Classic, your units have permadeath, but in Casual and Phoenix they'll come back. If I start out with Classic, lose unit XYZ, and switch to Casual or Phoenix, will I get unit XYZ back?
Yes, it appears that switching mode to Casual or Phoenix will resurrect the characters you lost in previous chapters (source).
This apparently only affects standard characters on your game path, though. Units obtained through capture or the Einherjar shop do not come back after switching from Classic mode.