Telstra at this time with still have responsibility for Priority Assistance (which really only says that a fault will be repaired within 24 hours), it is no guarantee that service will be uninterrupted even on a PSTN service. Optus are currently pulling out of their PA type system.
From the NBN Co site (https://www.nbnco.com.au/learn-about-the-nbn/what-happens-in-a-power-blackout/priority-assistance.html) "Telstra is required by the Australian Government to offer priority assistance services to people with a life-threatening medical condition. However, other phone or internet providers may also offer priority assistance (or similar arrangements) to their customers. More information is available from the Australian Communications and Media Authority (ACMA).
nbn has committed to support providers who give priority assistance services to customers with diagnosed life-threatening medical conditions. We will aim to provide the same connection and fault rectification times that customers registered for priority assistance currently receive."
Of course FTTN has the issue of power failure in your area, and as part of all Node installs they do now have Backup Batteries in them. So you can arrange some sort of Power backup in your relative’s home that will enable the use of their phone as long as the Node’s batteries last. This time of power at the Node is NOT guaranteed by NBN Co. and why they also insist on a mobile phone being available for emergencies.
Of what maybe of interest to you is that some newer DECT type phones have some backup power that allows them to work in the event of a power failure and then you would only need to find a power backup solution for the modem rather than for both the phone and the modem.
For your perusal:
https://www.uniden.com.au/product/bp-100/
on the above tick the “Operates during power outage” box to list the phones that work in a blackout.
