The short answer is no – there is no law that says that you need to pay a former employee indefinitely. If they are unable to find anything though, it may lead to a longer notice period.
The legal threshold revolves around how long it would reasonably take a person in similar circumstances (of similar age, experience, same nature of work, in a similar job market) to find comparable employment. There is no exact science to determine this length of time. There is, however, a great deal of judge-made law on which the courts will assess what the reasonable notice period should be. While that number has climbed in recent years to account for older employees who may have been in a single workplace for several decades, it still rarely goes beyond 24 months, and even those cases are exceptional circumstances.
Remember, a well-written and frequently reviewed employment contract can help limit these payment obligations, and can reduce a period of two years or more down to a matter of weeks.