only if it says so in his small print,lots of insurance companies do allow it,but a lot do not,he better check.but its advisable to insure the car as it will not be covered for fire,theft etc,if you let it run out without renewing it
And as soon as he gets out of the car it will be an uninsured vehicle, so he won't be able to park in public car parks, on road and so on.
Most insurance companies no longer allow 'other vehicles' on their comprehensive policies, and of those that do specify 'emergency only' and insist the other vehicle is fully road legal - which means is insured in its own right.
Ethel is correct, and don't forget that the Driving Other Cars extension on your policy is for emergancy use only - if your other half has an accident, he needs to have a very good excuse or the insurer won't pay for any third party damage caused