That's interesting in regard to remnant genes. The Black Robin is thought to have undergone repetitive genetic filtering from past events [1]
What I was thinking of was more along the lines where after a species faced extinction, what survived was due to slight genetic variance that in time the more successful would continue to push the more purposeful genes to adapt to the changes inflicted onto the area they inhabit or migrate more. I am of course not saying this is the instance in every population wipe out and re-emergence, I can point to instances where a simple change of behaviour comes down to learned behaviour, such as what happened with the introduction of cane toads and wildlife including birds learning how to eat the mongrels (carefully.)
The Paradise Parrot I would guess succumbed to the introduced rats ... and given their ground dwelling and termite nesting would have later faced the feral cat explosion. It is a pity.
I suspect in my immediate location only a couple of miles from a large forested area that was never heavily logged and now protected, that a small handful bird species remained unrecorded even if they were recognised by some common name by the immediate locals. The one bird species I'm still trying to identify had a simple call of individual loud chirps from high in octave to low and then half repeated from mid octave - it seems terribly unfamiliar to any one I've asked who I'd expect is familiar with all of the regions birds.
[1] https://en.wikipedia.org/wiki/Black_robin
"... leading to speculation that the species has passed through several such population reductions in its evolutionary past, and has lost any alleles that could cause deleterious inbreeding effects"