There are some court cases involving this issue. Also, there may be future legislation that defines whether inmates are eligible for CARES Act payments or payments made under a later round. See

https://procedurallytaxing.com/summary-judgment-victory-for-incarcerated-individuals/

Even if an employer-employee relationship exists, wages paid to prison inmates may not be subject to FICA taxes if the employer is a state or local government entity. The law excepts services performed by prison inmates in the employ of a State, political subdivision, or wholly owned instrumentality thereof from employment for purposes of social security tax. [Section 3121(b)(7)(F) of the Code]. The law also excepts such wages from the Medicare tax. [Section 3121(u)(2)(B)(ii)(II) of the Code].

This exception does not apply, however, if the inmate is performing services in the employ of a nongovernmental entity (for example, a private corporation operating a prison). Thus, whether amounts paid to a prison inmate are subject to FICA depends upon whether an employee-employer relationship exists and whether the inmate is employed by a government or a private employer.

See

https://www.irs.gov/pub/irs-wd/12-0016.pdf