Mail is considered sacred in a prison, detention center or jail and it will get delivered when an inmate is in administrative segregation, the SHU or "the hole". They can also get money into their account but the actual spending will be somewhat restricted to a limited amount of items at the commissary.
https://www.inmateaid.com/ask-the-inmate/do-inmates-still-receive-mail-when-you-are-in-the-hole#answer
Accepted Answer Date Created: January 27,2016