Disclaimer: I Do Not Own HHarry Potter.
He should have killed Delphi he sees that now it's late. She wasn't in Azkaban long before a group of Death Eaters broke her out and took her out of the country.
He tried to track her down, but he failed. Ten years she did nothing and yes he foolishly hoped that she never would.
The first attack came in the middle of the night. No one was expecting it.
Two hundred died that night, Ginny and James were two of those people.
People looked to him the way they look to Dumbledore when Voldemort rose to power and like Dumbledore there was nothing he could do. Still, he tried.
He learned early on that Delphi goals were different than Voldemort's, she didn't want to rule the wizarding world or live forever.
She just wanted to destroy as much as she could for as long as she could.
They were all gone Albus, Lily, his nieces, nephews, his friends. She let him live for the same reason Voldemort let Dumbledore live for his long as he did.
Because an opportunity hadn't presented itself to kill him yet, to show him, and boast of she's done, and fear.