I know this is kind of an "Uhm akctually" comment and i apologize for it, but we do actually know what happens to sinners who die. they uh... Dont. or at least they don't permantly if they're killed by anything other than angelic weapons, they're functionally immortal, they essentially just respawn (I'm pretty sure they just fall from the sky naked like the recently deceased guy does in the hazbin pilot does before he's hit by a car), though we've never seen this respawning on screen it's word of mouth from the series and the series creator. the reason for the exterminations in the series is to cull the immortal population of hell because heaven fears that sinners in enough numbers can rise against heaven. now hellspawn like Blitzo, Moxie, Millie and loona assumedly just... die because we have no idea where they go after that point.
Not that it really changes much narratively speaking beyond a couple lines of dialogue, if anything it makes more sense Blitzo would hire a sinner if he could considering the immortality, no need to theoretically pay hell health insurance if your employee just respawns. i just thought I'd let you know if you weren't aware based on the Millie dialogue about the player finding out if there's an "After-Afterlife".