This is an example of singular "they", which is increasingly being used as a non-sexist pronoun (which I think which we've discussed before).
However, the second sentence somewhat ruins the effort.
It was traditional to write "a person continues to live his life", but feminists asked why "him"? Why is a person always assumed to be a male unless otherwise indicated. You never saw a sentence saying "a person continues to live her life" to mean both sexes.
So someone came up with the variants of "they", and they have become so accepted that an authoritative dictionary can no longer deny that they now occur in (some) standard use.