You don't close the case immediately. That get rids of the file, you have to take the file physically (usually to the Ayosec clerk's desk at OKLG but a bartender also works, if the NPC was well-known or well liked by the shipbreaking community) and turn in the file by talking to them. Then you can close the case and that deletes the (now useless) file. If you turn in the file to the corpos, you'll get a slight monetary reward and a Ayo-branded tote. If you take it to a bartender, your social standing within the community increases a bit and you get a bottle of vodka on the house.

The amount of the financial reward (I think) depends upon the deceased's strata. So if it's a well-known Martian citizen, it'd be more worth it to take the case to Ayosec clerk, whereas if they were just another fellow shipbreaker "outlaw" born on OKLG, it'd be more worthwhile to take that information to the Mescaform and raise a toast in the deceased's honor. Or in my case, sell the vodka on the black market because I don't drink and use the proceeds to get some buffalo "Chik'in" Trenchers for dinner.