Ezy do have a system in place to ensure, as far as possible, that crews do not fly with any required elements expired. Expiring licences, medicals, ratings, SEP items, recencies etc are monitored and flagged up automatically some time before expiry. Emails are normally sent to crew members as reminders for actions they need to take - licences and medicals - but training expiries are normally rostered in good time. Furthemore, at check in, expiry dates are listed and crews are required to confirm that they are correct at valid. Despite all this, people do somehow slip through the system. Perhaps they shouldn't, but they do.
I have no idea whether the former GB pilots are part of this system yet, or whether an existing GB system is in place, but it's pretty poor of the company to relinquish publicly any responsibility for licence validity. It may be an idividual pilot's responisibility to keep him or herself legal, but it's a company's responsibility to ensure that its passengers are flown by qualified, licensed and properly trained crews. That's why they check and hold such details in their files!
JB