We currently consume the Companies House API as part pf one of our business processes. On the Companies House search in the advanced search filter, it lists two additional statuses; Open and Closed . Searching for Open companies returns 12,630 results all of which are prefixed with BR and searching for Closed companies returns 6,059 results which are prefixed SE or BR.
Although open and closed are not listed as legitimate statuses in the API documentation even though of the Companies House website it is possible to search for both. It is unclear whether these statuses are the same as active or dissolved but only they seemed to be only assigned to companies that are UK Establishment or European PLC types.