If it’s not airworthy then why would it be registered?

If it’s not airworthy and not registered you cannot rob the spares from it.

Some airlines park up aircraft from service, then rob them of useful spares to support the remainder of the fleet, but to do this and keep track of the parts they must remain registered, albiet not nessecerily as airworthy (for insurance purposes).

This is particularly done by companies operating older generation aircraft where spares sometimes have to be manifactured individually as their production has ceised.

Hope the above makes sense to you!