My Lydia got killed by a dragon, and I didn't realize she had died until I'd fast-traveled away and back about three times looking for her. So I put on my roleplaying hat and gave her a heartfelt lore-accurate funeral in the nearby river.
And yes, a step in that funeral may have involved taking all the useful gear she had, but it was in character, dammit.
In all seriousness, losing her actually did tear me up a little. I didn't take another follower for about two months, and I heal my new one, Kharjo, constantly and reload saves if he dies.