Back in the day we were approved to fly overlay approaches with the underlying navaid inop with just classic 737s on DME/DME updating alone (no GPS installed, the TAWS had its own GPS not connected to the FMC), as long as ANP was below 0.3 NM. Never had to do it, but it was a point in our books. That provision carried over to the NGs (and yes, the A320 as well: ACCURACY HIGH sufficient), but still, never had to do it in the real world. That said, more recent opened airports do not have a conventional NPA as backup anymore, just RNP approaches.