Why can it not be what the criminal (why the quotes I wonder) deserves? It might also be about reformation (certainly not redemption). but it is primarily about desert. And willingness to forgive has nothing to do with desert. The question for the sentencing judge is whether to give the criminal (no quotes) what the criminal (no quotes) deserves, or whether there are mitigating circumstances.
In the broader scope of societal incarceration a criminal is subject to the willingness of the system to "forgive" his/her trespasses. This is a purely functional assessment. The overlying ideology may be about redemption or rehabilitation, but the raw function of the system is retribution and subsequent forgivness. The criminal has no real power to lessen her punishment except that which is already systematically institionalized. Also the "deserving" of a second chance is already instituionalized and represented by the parol system.
No well adjusted person is going to give an unconditional second chance to someone who has seriously offended them. One of the few groups of people who do that are abused women. The institutionalized system however, represents a people as a whole and a people's general ideology in regard to criminals in general.
As a father I may forgive my child a serious trespass but I am thereafter on continuous guard for like offenses. They, no matter how much I love them and want to trust them implicitly, are not given an unconditional second chance, whether or not they get an actual punishment for their trespass.
Thus forgiveness is really not an unconditional second chance but a conditioned parol both institutionally and in most personal cases. It is a response to the desert of the incarceration or punishment not the desert of the offender's supposed rights to move on. The conditional parol is given by the offended party not earned or taken by the offender. The crime has been punished and thus there is no more reson for incarceration, just conscientious monitoring against recitivism.