ive personally VIC tested 1 cat a, and 3 cat b cars in my time at vosa,

there is no legal reason why a cat a or b car cannot go back on the road. the cat marker is an advisory from the insuruer and legally means nothing. The only point of no return for any car is when it gets issued a COD msrker, certificate of destruction, these are issued against the car upon its destruction

if the owner has cut the id out, hes a twat, as you can ring vosa and book a vic check for a cat a or b, and the dvla will issue a new v5