I had a household where I had one sim and she made herself a servo army, (so 7 servos). She died of old age eventually. They are all still there. They do break down around town, even though they can repair themselves (and each other) they don't seem to. When I see them about the town broken, whatever sim I am currently playing, I just have them repair them or call a repair man. I haven't witnessed any servo deaths in public, yet.
But yes, they can live alone. I've even given them a dog now that their "maker" has died.