The final non-flashback appearance of Carey was in State of Flux, where he was last seen being confined to quarters. I just assumed they forgot to let him out again until season 7, and he passed the time building that ship in a bottle...
JANEWAY: "Chakotay, I've been going through the crews' personal messages that Starfleet relayed to us, but I think they've made a mistake - who's this Ensign Carebear we keep getting letters for?"
CHAKOTAY: "It's Carey, Captain, Lt Carey."
JANEWAY: "Right, right - who is he?"
CHAKOTAY: "Surely you remember - curly-haired guy engineer guy? He was quite prominent in the first few months after we got stuck out here."
JANEWAY: "I barely remember what happened the previous episode, never mind six years ago. Remind me."
CHAKOTAY: "Well, he stopped a warp core breach the Caretaker caused, saving the entire ship and everyone on it, and you rewarded him by screwing him out of the Chief Engineer's job and giving it to B'Elanna. After she'd broken his nose."
JANEWAY: (laughs) "Yeah, that sounds like something I'd do. Wish I could remember it. So what happened to him?"
CHAKOTAY: (thinks) "If I remember correctly, we confined him to quarters during that whole business with Seska defecting to the Kazon, just in case he was the spy."
JANEWAY: "Wise precaution. Did we ever let him out again?"
CHAKOTAY: *thinks for a long time, then shrugs*
JANEWAY: "Oh. Oh dear..."