I can only speak for the airline I worked for until recently. We had a computerised company system which monitored all recency and licensing requirements and would generally look after you. But like all systems it had a human data input element which was open to error. A friend of mine found out the hard way after discovering that he had inadvertently flown while out of a legal requirement. He did the honest thing and self reported, only to have a severe disciplinary procedure thrown at him. It clearly stated in the company manuals that it is the pilots responsibility to maintain legality and they took a dim view of his oversight.