My grandfather was actually born in 1888. I was very young when he was alive, but I knew him for the first decade of my life. And because I actually knew someone born the 1800s, it's quite strange to imagine that nobody from that century is still alive.
Emma Morano turned 117 years old in November. She'd been born in 1899. Now she's gone, and so is everyone else born in the 1800s.
I'm willing to bet it will be more than 100 years before the last person born in the 1900s is gone; with scientific advances, maybe a lot more.