Funerals: Each time you fight someone there is a chance that you will be invited to attend the funeral of the mob member who gets killed in the crossfire of a mobster you are attacking.
If you attend, you will receive a Lodestone charm that helps you gain more money from missions. This is one time that you will want to be sure your target receives notification. You are hoping they see the notice and come running back to the game.
In addition to the lodestone reward, if the person being honored (the funeral of the dead guy) comes back to the game both they and you (who posted the invitation) will receive a Scythe. This item has an attack of 24, a defense of 12 and can be equipped on your avatar. The dead mobster should click on the published link on your profile page.