I guess it depends on what courts decide is the "standard of care" in prisons against transmissible diseases. This has been litigated in various way recently, not just following deaths:
From a legal standpoint, many the cases center upon: due process claims under the Fourteenth Amendment, particularly related to pre-trial detainees; Eighth Amendment protections against cruel and unusual punishment; Americans with Disabilities Act violations; and discrimination claims under the Rehabilitation Act. Plaintiffs are often asking judges to intervene to force immediate changes at prisons and jails, while litigation is pending.
The approach has yielded mixed results thus far. Some judges have moved aggressively, ordering institutions to improve conditions and to do more to adhere to CDC guides. Yet those decisions have met with continued appeals and resistance from corrections officials, and the U.S. Supreme Court has twice overturned efforts by federal judges to intervene forcefully in coronavirus-related matters.
In May, the high court rejected on procedural grounds a request by inmates to increase cleaning and COVID-19-related education efforts at their Texas-based geriatric correctional facility. The court upheld the U.S. Court of Appeals for the 5th Circuit, which had overturned a Houston-based federal judge’s ruling supporting the prisoners. A few days later, however, the court appeared to switched course, letting stand a federal judge’s order requiring that prison officials move hundreds of inmates from an Ohio institution where nine people had died from COVID-19. Then, on Aug. 3, justices, in a 5-4 decision, overturned a lower-court injunction requiring stricter health and safety measures at the jail in Orange County in Southern California.
The Orange County case, Barnes v. Ahlman, is instructive in terms of the arguments being made on both sides and the response by the courts. The jail’s leadership was accused by prisoners of ignoring Centers for Disease Control and Prevention recommendations by failing to enforce social distancing measures and declining to isolate inmates with COVID-19 symptoms. A federal judge in California had issued a preliminary injunction that required the jail to take stronger measures, and the U.S. Court of Appeals for the Ninth Circuit declined a request by the jail to halt the injunction.
Jail officials argued that, prior to the injunction, CDC guidelines had been “largely implemented” and said the injunction’s requirements far exceeded the scope of the CDC’s recommendations. They also cited their efforts to voluntarily release half of the jail’s inmates to help with social distancing and said they had all but eliminated “COVID within the jail population.”
The Supreme Court majority voted to stay the injunction while litigation continues. As is custom, the justices did not explain their reasoning in the order. Justice Sonia Sotomayor dissented, saying the stay was premature and that jail had placed inmates at significant risk. Earlier in the Texas case, Sotomayor encouraged lower courts to ensure “that prisons are not deliberately indifferent in the face of danger and death.”
I guess some Supreme Justices might not say it but probably think it that it's not cruel and unusual to (catch and) die of transmissible diseases in prison since it happens all the time.
E.g. according to one study 97% of infected inmates don't get Hep C treatment.
At the other end of the spectrum:
a former jail administrator in Oklahoma was sentenced to more than 4 years in prison following his decision not to take an inmate with diabetes to hospital, resulting in his death in 2013.
The administrator "pleaded guilty to one count of deprivation of rights under color of law." The inmate in question died of ketoacidosis. So the standard of care in prisons is somewhere in between these extremes.
Most litigation regarding Covid-19 seems to center on whether CDC guidelines have been followed or not. I see that the CDC does have some specific guidelines for correctional facilities in this regard.
I'm not sure of negligence case law in prison, but regarding the 8th Amendment violations, Helling v. McKinney is probably relevant to preventative measures:
In Helling v. McKinney, the Court considered the case of a Nevada prisoner, "the cellmate of a five-pack-a-day smoker," who sought to be housed in an environment free of second-hand smoke. McKinney suffered from no ailment and sought no medical treatment.
Justice Byron White wrote for a 7-2 majority of the Court that McKinney's claim that prison officials "have, with deliberate indifference, exposed him to levels of ETS [second hand smoke] that pose an unreasonable risk of serious damage to his future health" raised a valid claim under the Eighth Amendment. He wrote that McKinney would have to prove both the scientific facts of the dangers of exposure to second-hand smoke and prove that community standards supported him, that "it violates contemporary standards of decency to expose anyone unwillingly to such a risk. In other words, the prisoner must show that the risk of which he complains is not one that today's society chooses to tolerate." He would also have to prove that prison officials acted with deliberate indifference.
Also following Ashcroft v. Iqbal
government officials could not be held liable for the unconstitutional conduct of their subordinates
so each official would have to be proved liable individually for involvement in such a (faulty) decision.