Alice's "deletion" is purely ceremonial. Everyone knows that she existed, but no one speaks of her in polite company.
Alice is not executed but imprisoned. (They still erase all records of her existence.)
They simply edit the records so no one will know that Alice was a criminal. If she was executed, the records will say that she died in an accident or mysteriously disappeared.
The chance exists that Alice's deeds, even if she died from them, would make her a martyr in some people's eyes and inspire rebellion if word got out, and the government in power wants to forestall that possibility.
Alice erases all the government's records of her existence, either in order to hide from them or as a way to further scare the crap out of them when she attacks them as a one-person army and no one in power even knows who the hell she is. It also has the added benefit of protecting her loved ones - the authorities don't know whom they should harass or threaten, and openly threatening everyone tends to be counter-productive.
The police hand weapon is a big black pen. When someone robs a bank, policemen bring their pen: "hands up or we erase you!"
A government desk jockey accidentally deletes Alice's profile, nobody remembers her.
Zig Zagged: All of the records that Alice are obliterated, and her family is brainwashed into believing that she never lived in the first place. Then Alice escapes, and everyone thinks she is some kind of crazy person. She gets put into a mental hospital that is just as bad or worse than the prison.
Averted: No records are deleted or messed with in any way.
Lampshaded: "You might as well take the photo albums while you're arresting me."
Exploited: Alice escapes and starts in a new place with a new identity in order to open the bakery she's always wanted.
Defied: Alice makes sure that she has extra copies of pictures and records because she joins La Résistance.
Discussed: "All this danger might make you a little paranoid, but everyone will remember you if you escape."
Conversed: "Ever notice how whenever a member of La Résistance gets captured, they always delete all memory of him?"
Implied: Alice escapes from prison, and her own friends and siblings have completely forgotten about her.
Deconstructed: "They erase all evidence of enemies of the state. However, they aren't so effective in actually disposing of them physically. Every once a while, a man with nothing to lose jumps off a prison train and vanishes in The Lost Woods, or runs for the hills some hours before the midnight knock, or crawls out of a pile of shot bodies and scampers off into the night, wounded but alive. They all resurface here, in La Résistance. Right now, we've got a cadre of untraceable avengers, about whom the police knows nothing at all: neither addresses, nor fingerprints, nor their vulnerable loved ones. They are invisible, they are lethal, and they have no other place to go, and soon we'll have enough manpower to shoot the Dictator's mooks from behind every corner".
We deleted all evidence that the entry for Unperson ever existed.