With a few exceptions, public entities are immune from liability for injuries caused by any prisoner to another prisoner while an inmate of a “prison, jail or penal or correctional facility”

Gov.C. § 844.6(a)

“Notwithstanding any other provision of this part, except as provided in this section and in Sections 814, 814.2, 845.4, and 845.6, or in Title 2.1 (commencing with Section 3500) of Part 3 of the Penal Code, a public entity is not liable for:

(1) An injury proximately caused by any prisoner.
(2) An injury to any prisoner.”

This also applies to claims that derive from any injury to a prisoner—i.e., public entities are immune from loss of consortium liability to an injured prisoner’s spouse (or registered domestic partner) and from wrongful death liability to the prisoner’s heirs.

Therefore, there could be no claim against the government institution, except for injuries legally caused by a public employee’s “negligent or wrongful act or omission.”

Gov.C. § 844.6(d)

“Nothing in this section exonerates a public employee from liability for injury proximately caused by his negligent or wrongful act or omission.”

To know if a prisoner may or may not have any claim against a public entity for injuries sustained while detained, it is best to consult with a lawyer who is an expert in personal injury cases.