Like humans, Sims are affected by a death of a family member or neighbor. Sims need to display their grief and pay their respects to the dead. But they do it in a somewhat different way, in that they don't have funerals.
When a Sim dies a tombstone or urn will appear in place of the body. You can move the tombstone or urn to a more suitable place or sell it. The tombstone or urn is a mourning place for the Sims. When they pass it, they will stop and cry. Some Sims will take much longer to pay their respects, while others will only take a few minutes. Generally the mourning will only last up to 48 hours.
Graves & Urns
As I mentioned above, graves and tombstones can be moved to a final resting spot for the Sim. However, if the family or you didn't like the Sim, you could always sell it for 5 simoleans. Neither tombstones nor urns can be bought, and once you delete one, you can't get it back.