If you purchased your ticket through a travel booking site, the terms and conditions may state that the travel booking site is not responsible for notifying you of the status of your flight. In this case, the buyer must check the flight status himself/herself. On the other hand, if you purchase a ticket through an airline's website, the airline will generally send information about flight cancellations to the e-mail address you registered. If you are concerned about a flight cancellation due to weather or a natural disaster, you should repeatedly check the flight status and airport departure/arrival information on the airline's website.