Nursing Home Demanding Full Month Of Medicaid Patient Liability For A 7-day Stay Upon Discharge. Is This Legal?

Location: Pennsylvania

Hi everyone, looking for advice on a Medicaid billing issue during my mom's nursing home discharge in Pennsylvania.
My mom is a disabled Medicaid resident. Her monthly SSI check arrives on the 17th, and the nursing home's monthly billing cycle starts on the 21st. We have a firm, safe community discharge finalized for October 28.
Because her new billing cycle starts October 21 and she leaves October 28, she will only be occupying a bed for exactly 7 days of that month.
I asked the Business Office Manager about prorating the bill so my mom has money left to live on when she transitions home. She flat-out refused. She is demanding the full monthly payment of $1,456.00 on October 21. She explicitly told me in an email that she is doing this to claw back "uncollected funds" from a separate HMO stay over a year ago (2024-2025), and openly admitted she knows this will leave my mom with zero money for food or shelter for three weeks until her next check.
I want to pay the facility fairly for the 7 days they are actually caring for her this month (about $328). My plan is to let the October 21 due date pass silently, go through her formal discharge meeting on October 26, and then log into their online portal on her actual discharge day (October 28) to manually pay just the 7-day prorated amount. I am also quietly reaching out to the PA Long-Term Care Ombudsman today for backup.
Can a nursing home legally charge a full month of Medicaid patient liability for a 7-day stay to collect old debts from over a year ago?
What should I expect at the October 26 discharge meeting if the bill is past due, and how can I protect my mom's discharge date?
Any advice or insight from people who have gone through this would be deeply appreciated. Thank you.