1881, there was a woman who was born in 1792, and died in 1903!
1897.... also, 1792-1903? That's not really shocking. That's only 111. There have been many people who have been born near the end of a century, survived an entire of the next century, and even still been living during the first few years of the following century.
Infact, there are 6 people alive in the year 2013, that were born between 1898, one of which is British, making her, the last surviving British resident to have been born in the 19th century. The oldest living person was born in 1898, making them exactly 115 years old this year.