You are responsible for obtaining a new international flight should you miss the flight to your final destination. In addition, if you decide to book a connecting flight you should make sure that the connecting flight is changeable. Typically these on-line airline booking agents (Orbitz, Travelocity, etc.) DO NOT allow changes to be made to flight bookings.
It will be important that if you are planning to extend your travels that you arrange for your ticket to be adjustable if necessary. It may cost some amount of money to change flight dates. It is your responsibility to make these arrangements and to investigate the costs associated with making changes.