Once the Vault Dweller has given Neal's urn to Vinnie, he will ask for the Dweller's help with killing Neal. If the action is accepted, he will be transported to the Skum Pitt. Once Neal and Trish (see note) are dead, the Vault Dweller receives 300 XP and negative reputation.
After the rendezvous with Vinnie at the bar, it is possible for the Vault Dweller to end "turn" throughout the combat sequence without being targeted; Companions will not interfere but instead move and not attack unless accidentally misfired at. The player character can choose to end combat after the outcome which almost always ends in Vinnie being killed. After returning to the Skulz hideout the player will be confronted with a respawned Vinnie who will accordingly say "Soon, Neal gets his, huh?" when interacted with. Oddly enough, revisiting the Junktown Casino section renders the camera to fixate on the bar with the dialogue and quest practically resetting without the player character's presence in the ordeal.
Even in the case that the Vault Dweller or Vinnie kills Neal and Trish, the Skulz can become hostile upon return to their base, a bug possibly stemming from Champion karma or the completion of the Stop Gizmo quest.
There is an exploit with this quest to gain infinite experience and negative reputation. Once Neal and Trish are killed, exiting to the south and reentering the zone with the Skum Pit will keep displaying "you gain 300 XP for putting a cap in Neal's ass, you Skul" and rewarding the player with 300 XP and -1 reputation. If you wait a couple of hours to trigger this exploit, reentering the Skum Pit zone will also reset the time to when you killed Neal.
If you initiate combat before the dialogue between Vinnie and Neal completes, the Skulz won't help you in the fight. Although killing Neal and Trish will still complete the quest, granting 300 XP, you will only get -1 reputation instead of -6.
Trish does not have to die to complete the quest. If Neal has low health and runs out, it is possible to end combat once Neal dies outside of the Skum Pit when the Skulz chase after him. Trish will still be alive, and you will be awarded completion of the quest.