Arthur and Chloe died every day; more specifically, every night the current version of Arthur was killed by hundreds of other versions of Arthur. The next version would come to the window and knock, and the current version would go outside to meet his fate. The same thing happened with Chloe and with Henrietta, their hen. Arthur was obsessed with finding the best dying words, and spent each day poring through a book of quotations to find a great one to use.
When the Sixth Doctor came to the bed and breakfast, he too became involved in the daily deaths. After several days, he finally decided not to go the window when his next self knocked. The cycle of deaths was ended. Arthur and Chloe resumed their normal lives. (PROSE: The Death of Me)