I think thr deletion is meant to be instantaneous, this means that deleting someone would not trigger their deletion.
Although law enforcement would be much nonexistant, the loss of protection that it losing it gives would be worth enough to deter the majority of cheap assassins.
Also, what would happen to currency? Banks would be useless as they are too easy to take over, money could only be exchanged in small amounts. I dont see anything that would be incredibly valuable (like a house or boat) being made as someone could literally just walk up and take it. It is unikely that the owner would value the deletion over the house, as them they have lost their only means if protection.
Finally, i see a division into 3 castes: those who have lost their deletion, those who have or pretend to have their deletion, and some small groups that reject deletion.
Those without one would be bullied and even enslaved by the ones with it, until those without got numbers to overrun their captors, causing them to lose their deletion and thier life.
People who still have theirs would most likely form small, tight groups to minimize the rusk of a murder chain, wheras those without would have to travel in packs to prevent enslavement
The hardest question for me is whether there would be more people with or without their deletion.
EDIT: whoa, didnt really mean to make such a wall of text. Might need to trim it down