Just wondering about this. Sometimes you see a man running past outside the cities just named Thief. Is there anything to worry about with them? Do they steal from you if your not careful? Or is it like when you see a group of high elves(thalmor somethings) arresting a stormcloak that if you ignore them they will ignore you and you will soon never see that particular person again?

It's a one of a number of possible random encounters in the Story Manager, similar to the Thalmor group escorting the Stormcloak prisoner.

I usually find one coming out of a NPC home and getting attacked by the townsfolk. I never find anything that expensive on their corpse. I don't think the game is designed to have them break into your own home and steal stuff.

They usually hang by the side of the road to ambush you, they won't strike first but will demand that you give away your valuables, if you refuse they would attack but you could also intimidate or persuade, and I found persuasion to work most of the time, plus they're pretty tough at lower levels, dual wield and all..

Same here i mostly see them in Riften getting chased by guards and getting killed
They always seem to have better loot then i ever get from the same houses.(diamond on one of them)

You see them most often in Riften running around in the market and if you or the guards kill them nobody seems to mind you looting them afterwards. In the wilderness its normally someone who stops you and asks you to pay up and attacks if you don't. I love the random encounters. I think I'm seeing more than before with the Dragonborn DLC active and they seem less buggy.