There is no way there wouldn't be enough unemployed or underpaid women who wouldn't work in a women's jail as a guard, if for no other reason than the pay is far better than working at some burger joint for peanuts.
Women can't (and shouldn't) work as guards in male prisons ... so that's part of the problem.
The other part is America's whole gd judicial system is a clusterfuck, from manditory sentencing to outrageous bail, from falling-down jails to privatization of said prisons.
The whole system needs to get pulled into the 21st century.
So yes, you're right, there is a problem with staffing levels. But to keep on-keeping on without radically changing anything/everything is stupid ... and insane.
Women 100% work in men's prisons. One of the things that led to women getting hired in men's prisons was a shortage of men who wanted to work as a prison guard.