In order to tease out the nuances of this question I'm going to pose an extreme hypothetical:
A very successful performer leads a lavish lifestyle. He only wears clothes of fine cashmere, his diet includes beluga caviar every day, and he takes an expensive cocktail of drugs to treat a rare but serious disease.
Then he is convicted of manslaughter committed while drunk driving and sent to prison.
In prison, presumably, they do not care about his comfort and customs. He is only allowed to wear the prison-issued garments, however coarse they may feel to him. His dining options are limited to "regular," vegetarian, or Halal slop.
Presumably these privations are "features" of the punishment, and to the extent he suffers disproportionately from them the justice system has weighed that extra suffering in determining his sentence? Is there any precedent for a feature of incarceration being found "cruel or unusual" not generally, but in a particular case? E.g., "It's not cruel to make a peasant eat gruel – that's his normal diet in the best of times – but it is cruel and unusual to feed the same food to a king!"
Furthermore, the prison does not provide the expensive medical treatments he was undergoing. It cannot afford to. But, since he is being deprived of his income as a performer, the prisoner now cannot afford them either. I.e., his sentence is in effect not only to be incarcerated, but also to be deprived of some health- or life-sustaining support.
In the limit there is some duty of care to prisoners. For example, they cannot be starved to death, and must enjoy some level of medical care. But is there any precedent for suspending a sentence because it would adversely impact the health of a convict, as in this hypothetical?