Australian banks have a mandated 100% LCR and most banks hold 130%+ LCR (remember LCR is calculated based on a 30 day stress outflow).
Even if a run lasts longer than the period above they're backed mostly by mortgages that are priced significantly higher than their borrowing costs and LVRs that average lower than 80% and the way AU banks price interest rates will always cost significantly less than their borrowing costs. They're never going to have trouble raising money on prime, variable interest (average fixed terms are always less than 5 years here) debt.
APRA standards all but eliminate a sub-prime problem here. Loan affordability has been a very hot topic here over the last decade.