I'm a PRN nurse aide, but I guess our system is different than yours. At my hosptial PRN doesn't equal "on call," it means I work as my schedule allows. I put in my availablilty two weeks in advance, and my manager schedules me according to the hospital's needs on my available days. If I want to pick up extra shifts, I can call staffing any day a few hours before shift change and ask if they're going to be short, and the staffing clerk will either tell me no, or she'll put me down to work.
I get the occasional call from staffing when they're really really desperate (staffing also calls all other qualified employees, whether they be full-time, part-time, or PRN)...but if I can't come in, I can't come in. And honestly, if I could have come in, I would have put that day on my schedule as available, or I would have called in early and asked to be put on the schedule for an extra shift.
Are your PRN staff supposed to be able to just come in at a moment's notice? Do they get on-call pay? If so, those people need to be fired. If not, sounds like your facility needs to hire more full-timers instead.