Disgaea Wiki
D1 Grave example

The Hospital NPC replaced by a Grave in Disgaea 1.

A Grave is a placeholder object meant to show a dead unit.

When a hub NPC is killed in a battle (from Dark Assembly Proxies in Disgaea 1, or the fight with Friday MKII in Disgaea 2) they are removed from the main hub and replaced by a grave with their name on it. Characters that are important to the storyline are not present during the battle so they can't be killed. Shopkeepers, including the Item Worlder or Dark Assembly NPC, can be killed, resulting in their facilities becoming unusable.

If by some accident you kill one of the NPC's, a quick save and reload will fix the problem. The save and reload was mentioned in the official strategy guides for the game.

Disgaea 3 and Disgaea 4 have Grave objects that can appear in stages, and destroying one will spawn a Spirit enemy at its location.

In Disgaea 3 and Disgaea 4, a Grave is used to show a dead unit in the Classroom/Cam-Pain HQ and will remain until the unit is revived.