Sometimes thieves spawn in cities, and everyone including the guards participates in surrounding the guy and beating him down while he tries to escape. Then, once he dies, everyone turns and goes back to where they were before.

When I run up and loot him, he's got several septims and anything from a candlestick to a flawless gem, none of which are marked as stolen.

Neither the town people nor the guards who ostensibly were chasing him to recover the stolen goods actually loot these items from his corpse.

Is there any mod out there that makes NPCs loot a downed opponent or stop and search a corpse? There as a mod that did this in Oblivion. Was one made for Skyrim?

I'm not aware of any but it can be done with a bit of clever scripting...