Does not played sims leave a gravestone?

The circumstances for which tombstones/urns are spawned on a Sim's death are pretty narrow and homeless sims definitely don't spawn them when they die away from the currently active lot.

You could just summon the ghost using the summon sim cheat (I believe you need to use the one that summons by SimID for ghosts) and then ask it for it's urn, if you do want it. If you use MCCC, you can summon them from a mailbox just by clicking.

Edit: Here's a post that explains the codes needed to get a SimID and the summon sim by ID command, if you do want/need that info.
Further research also shows that being able to just ask for a urn might be tied to a mod I use, this thread has further info on how to still get a tombstone though.

But what happens if that sim is on a community lot when passing? I read about simmers searching for gravestones, but perhaps that was actively played sims that were just not played while dying.

It's not very important to me to find that stone/urn, I left the couple out of my active households for a reason. Just though that if the stone exists I'd move it to one of my graveyards. Thanks anyway! :)

Unplayed sims don't leave a tombstone at all unless they die on the currently active lot where your played Sims are, so there's no point in searching for it, no.

People who talk about hunting down gravestones are doing it for played sims which died when not being played. Even for those, I have a horrible track record in those tombstones ever being found (and Answers HQ has lengthy bug reports about missing tombstones). I use a mod to make sure i can easily get the urn/gravestone when I want it for that reason.