Cover After a Policy Runs Out

A long trip can easily outlast the original plan, especially when flights change or people decide to stay away a little longer. While comparing options for that scenario, I came across https://www.globelink.co.uk/al....ready-travelling-tra and found it relevant because it addresses travellers whose previous insurance has expired during the trip. Do most people check expiry dates early enough, or does this usually become a last-minute problem?