CAT C is a graded insurance write off in which the cost of repair was deemed to be greater than the worth of the vehicle. CAT C doesn't mean it has been in an accident it could simply have been flooded or some such. CAT C isn't all that different from CAT D as they are both economic write-offs which are deemed to have endured only cosmetic damage.
CAT C vehicles only require a VIC if not being retained by the current owner. VIC = Vehicle Identity Check it is not a certificate of roadworthyness or repair standard.
CAT C can represent a great bargain, but the circumstances of the CAT C grade are critical.
I bought an E61 5 Series Touring as a CAT C write-off as it had ingested water into the engine and the engine was valued at £15k. I replaced two bent conrods at a cost of £95 and 4 days of my time. The car was 65% under book.