So, after doing the Companions quest where you first encounter the Silver Hand I run all the way to Meridia's temple to do her quest as I found a gem that attracted her attention. When I reach the temple I realize Farkas is still following me. When I reach the final room with the necromancer boss, the door locks behind me with no way to open it, and after I've killed the boss and gotten the artifact, I'm teleported out.

I look around. No Farkas. Then it hits me; he's still in Meridia's inner chamber! A cruel fate, being trapped forever within the daedric temple, doomed to become its grizzled old draugr guardian for all eternity. I'm not looking forward to explaining this to Vilkas.

He might find a way out, eventually. At least the hirelings do even if you lose them in impossible dungeons.

Now, Farkas isn't the brightest of guys... Maybe Vilkas should make this your next rescue mission.

I wish this would have happened when he had the annoying bug, so he kept talking to you.