The question of whether it would be a crime to escape in that situation boils down to the "necessity" or "choice of evils" justification which applies only in extreme circumstances but might apply here.
As others have noted, that defense would apply only so long as it is actually necessary to escape to stay alive, after which someone would have to surrender to the first available authority. But, even if someone was technically guilty of "escape" the circumstances would no doubt influence how prosecutorial discretion was exercised and would likely result in a shorter sentence for escape to the extent that there was a conviction for that offense and the judge had discretion to impose a mild sentence or a sentence concurrent with out sentences that the inmate is serving at the time.
If a result of the disaster the state had more inmates than it had a capacity to house in other facilities or by relocating inmates to facilities in other states under a contract arrangement and the state could not secure a legal waiver of the limits on how many inmates it could house at a particular authority, it might have to release inmates (systemwide) of its choice until it had enough room to house the remaining inmates. Usually, in a situation like that, the state tries to release inmates who are fairly close to their release date and have good disciplinary records while incarcerated.
Also, the prison operators have a legal duty to protect inmates that arises under the 8th Amendment as incorporated against the states thorough the 14th Amendment and usually enforced in a lawsuit for money damages or injunctive relief or both brought under Section 1983.
A case discussing the duty in the context of medical care (which applies equally in the case of a natural disaster) says this:
The Eighth Amendment imposes a duty on municipal actors to “provide
humane conditions of confinement.” Makdessi v. Fields, 789 F.3d 126,
132 (4th Cir. 2015). In order to state a § 1983 claim under the Eighth
Amendment for inadequate medical care when in confinement, a plaintiff
must allege that municipal actors were deliberately indifferent to his
serious medical needs. See Estelle v. Gamble, 429 U.S. 97, 104 (1976).
“[T]here is a subjective and an objective component to showing a
violation of the right. The plaintiff must demonstrate that the
officers acted with ‘deliberate indifference’ (subjective) to the
inmate’s ‘serious medical needs’ (objective).” Iko v. Shreve, 535 F.3d
225, 241 (4th Cir. 2008) (quoting Estelle, 429 U.S. at 104).
According to the Supreme Court, the deliberate indifference standard
lies “somewhere between the poles of negligence at one end and purpose
or knowledge at the other” and equates to recklessness. Farmer v.
Brennan, 511 U.S. 825, 835–36 (1994). Allegations that a municipal
actor knew of and disregarded a substantial risk of harm are
sufficient to state a claim for relief. See id. (“It is, indeed, fair
to say that acting or failing to act with deliberate indifference to a
substantial risk of serious harm to a prisoner is the equivalent of
recklessly disregarding that risk.”); Parrish ex rel. Lee v.
Cleveland, 372 F.3d 294, 302 (4th Cir. 2004).
A more generous standard of liability for the prison operators (if I recall correctly, "negligence" rather than "deliberate indifference") applies in cases where the inmate is detained prior to conviction while awaiting trial, or for a purpose other than a criminal conviction (e.g. due to a mental health hold, protective custody, awaiting deportation where criminal immigration violations are not alleged, or curfew violations).
The standards for holding the governmental entity itself liable is different than the standard for holding the individuals operating the prison liable (and additional 11th Amendment issues of substance and forum come into play that require suit to be brought in state rather than federal court on such a claim when the governmental entity owning the facility is a state government) (per the same case linked above):
In order to state a § 1983 claim under the Eighth Amendment for
inadequate medical care, a plaintiff must allege that a municipal
actor was deliberately indifferent to his serious medical needs. See
Estelle, 429 U.S. at 104. A municipality, however, may not be found
liable under § 1983 “based on a theory of respondeat superior or
simply for employing a tortfeasor.” Hill v. Robeson Cnty., N.C., 733
F. Supp. 2d 676, 683 (E.D.N.C. 2010); see also Riddick v. Sch. Bd. of
Portsmouth, 238 F.3d 518, 522 (4th Cir. 2000). Rather, to state a §
1983 cause of action against a municipality, a plaintiff must plead
“(1) the existence of an official policy or custom; (2) that the
policy or custom is fairly attributable to the municipality; and (3)
that the policy or custom proximately caused the deprivation of a
constitutional right.” Pettiford v. City of Greensboro, 556 F. Supp.
2d 512, 530 (M.D.N.C. 2008) (citing Jordan by Jordan v. Jackson, 15
F.3d 333, 338 (4th Cir. 1994)); see also Carter v. Morris, 164 F.3d
215, 218 (4th Cir. 1999) (holding that a plaintiff must allege that a
constitutional violation was caused by a municipality’s “official
policy or custom”).
The prison operators could also be subject to federal criminal charges for violating the civil rights of the inmates for abandoning them in a natural disaster, and quite possibly also various states charges related to official misconduct.
