Yes, inmates diagnosed with sleep apnea can and do use CPAP machines inside correctional facilities. It is a medically necessary device for a documented health condition, and facilities are required to accommodate legitimate medical needs. The process typically involves getting diagnosed or having an existing diagnosis recognized by the facility's health services, and then having the equipment approved and issued or retained through the medical department.
On whether they get to take it home at release, that is where it gets less clear. If the CPAP was provided by the facility, it is technically institutional property and may not be taken by the inmate. If it were their own machine that was allowed to be kept, the answer may be different. The specific outcome depends on the facility's policies, who owns the machine, and what the health services staff determines at the time of release.
The best way to get a definitive answer for a specific case is to have the inmate ask their case manager or health services coordinator directly, ideally before the release date, so there is time to arrange continued access to the equipment either by keeping the machine or by making sure a replacement is set up through community healthcare before they walk out.
Going without a CPAP after relying on one is a real health risk, so getting that question answered ahead of release is worth prioritizing.