The death of Emma Morano meant that in a way the 19th century finally ended. As well as being the oldest living person in the world (until she died of course) she was the last living person born in the 1800s, born late in 1899 infact. Her successor as oldest living person was born in 1900.
However Morano would not have had any memory of the 19th century, the century passed out of living memory (something i am very interested in) some time ago. I think you probably have to be around 7 or 8 at least to have any meaningful memories of your surroundings. Although you usually do have earlier memories you tend to be more interested in toys or food in your earliest years. Although i was born in the early 1970s i have few memories you could say were living memories of the decade, maybe some around 1978 or 9.
Looking at the records for the oldest people the oldest people born in around 1890 its possible that Emiliano Mercado de Toro born in 1891 and died aged 115 in 2007 was the last person having much in the way of living memory of the 19th century.
Everything passes out of living memory eventually of course, the First World War no longer has any living combatants though there are still people around who might have living memory of living in those years. Or not, memory is a very unpredictable thing. I lived during punk but i couldn't tell you anything about it!
I wonder when the last person born in the 20th century will die and when that decade will pass out of living memory. Its likely to be some time in the next century though maybe with scientific advances it could be a lot later than that.