I'm talking about the legal position, i.e. what a court would do, not necessarily what your insurance company will tell you.
Consider a hypothetical situation in which your insurance 'ran out', you failed to arrange alternative insurance but continued to drive your car on the roads.
If you were to cause an accident which, say, paralysed a promising athlete, if its at all possible, a court would bend the law to say that you are still covered by your 'previous' insurer.
In reality, the insurer would charge you for the premiums between the date of the policy lapse and the accident and then pay out the third party element of the claim (personal injury, and potentially damage to property of the athlete)
Obviously, this is a very questionable legal outcome as there was no official contact in force. The courts have specifically created this artificial legal situation to protect the hypothetical athlete.
There are lots of legal situations like this where, for policy reasons, Judges effectively decide what is a just outcome and work backwards from that, selectively applying law to create the outcome they want.
Its not beautiful, but it is generally done in the interests of justice, or protecting public finances (limiting negligence claims on police/ the NHS etc).