If you mean "can I use the API to search for all companies dissolved from 2016 onwards and return their numbers?" then (unless CH have added a new advanced search to the API) the answer would seem to be no. See search docs:
See also about experimental "address search": http://forum.aws.chdev.org/t/for-search-companies-query-what-does-it-search-and-how/1007
The API is designed for searching by name (fuzzy search) or number. Of course it will return information on company status for all companies your search finds and if and when they ceased.
If you want to find all companies which were dissolved from 2016 onwards and only need to get this data once, or updating it monthly, you could use the downloadable data product:
This is a monthly snapshot in CSV of current company data.
The data format is documented at the link (rather basic).
The fields of interest to screen out dissolved companies would be:
If you were just wondering whether dissolved / ceased companies were reported on, the answer is "yes" if they ceased up to 6 years ago. See:
Specific information is in the change note:
"Dissolved company names. Dissolved company names are now considered, but are given less significance than equivalently matching active company names. The last six years of dissolved companies will be available."
"...but unless you are pretty closely matching the dissolved company name, it will be ranked less important than an active company, as a decay function of it's dissolution date."