That wouldn’t make any sense.
I don’t know, but I’m guessing a reason for offering 2:1 for time spend remanded, would be that time in remand would be time held before actually being convicted of a crime. So, a justice-oriented reason.
Giving a discount on jail time for voluntary stunt suffering seems like the person suggesting it thinking jail time is about an amount of suffering. I don’t expect that’s the case, though I suppose some cultures might approach it that way.
An idea that seems more relevant to me, might be for the prisoner to offer to spend their time making amends to whoever they harmed (in some welcome way that wouldn’t annoy (and might even require the approval of) the victims), or other deeds that would tend to indicate the prisoner is rehabilitating themselves. This is done, in the sense that some prisoners get their sentences reviewed sometimes, taking into account their good behavior in prison.
In one culture in a fictional setting in The Warlock’s Workshop, an adventure in The Fantasy Trip game, people caught for crimes may be offered a choice of punishment, depending on the crime, amount of harm the criminal did, and who caught you.
For example, there’s a merchant caravan that might offer the choice of trial by combat, or a speedy beheading. Or if you didn’t kill anyone yourself, you can choose to have a hand cut off and being left in the desert with only your clothes and a waterskin. Or, you can keep your hand, but be flogged unconscious and left in the desert naked and with your hands tied.