In modern society the main punishment for a crime is either imprisonment or financial penalty. Even if you're a billionaire, a 20 year prison sentence isn't something to brush off, and a large fine may be a big disincentive.
Suppose people could live arbitrarily long lives. Now a fixed term prison sentence (of any duration) can be shrugged off by many people since there's always another 200 years where that came from, if the person wants it. A monetary penalty can also be shrugged off, they can build up a new fortune some way or another in the next 150 years. A variable length sentence ("until no longer a risk" or "X strikes and out") is trickier but most crimes don't get that nowadays, and its tricky to assess rehabilitation. And of course most crimes don't merit death.
In this question I'm sticking very close to current society, so the kinds of crime and punishment seen are quite close to today's. As arbitrary lifespan is now almost universal, criminals are becoming noticeably more relaxed about 5-15 year prison terms for assault, or 8 years for hacking and spam emailing, or yet another sentence for shoplifting, which lack the deterrent and protection ability they used to have. The Law Society or some other body puts out a consultation paper seeking public input how criminal sentencing should respond to this.
Human rights mean that, as happens today, a persons health isn't a valid target for punishment, so limiting their 'natural' arbitrary lifespan or otherwise targeting their health isn't going to be allowed, and of course too-cruel punishments probably won't be allowed by legislators either. The expression "life sentence" is a particular issue as life duration is arbitrary and at the criminal's choice; they may not be viable any more, or not in the same form (also its too close to "imprisonment until person commits suicide": imprisonment until death may be technically viable but the courts may see it as unreasonable in most cases as it's too arbitrary and raises the question of death by what means). Overall they're probably looking for evolution not revolution in their response, if possible, but are also looking for whether prison and financial penalties can actually work as they have in the past.
What kinds of plausible responses might be received, and what plausible ways could formal criminal punishment adapt to arbitrary lifespan, especially for less dramatic and "everyday" crimes?
Update - the arbitrary length lifespan itself is "just how it is", so there are no drugs or medical procedures maintaining it to target, and targeting health wouldn't be seen as acceptable anyhow (as said above).
(If it helps, I think an acid test for any answer might be the thought experiment "Suppose this was an actual formal consultation by the Law Society, in current society.....", which should help to separate relevant and even revolutionary answers from answers that don't really fit the criteria. But maybe not)