I've seen Ca(OH)2 be used to dehydrochlorinate (-HCl) trichloroethane to obtain vinylidene chloride. That has a great double bond there to polymerize into a chlorinated polyethylene. I'm sure NaOH would have a similar effect as Ca(OH)2 if not act even better.
That would be reasonable, but I'm sure the polymer didn't contain chlorine. As I burned it, it smelled like a paraffin, not like PVC. Meanwhile I know that some polymers containing oxygen, for instance for hot glue guns, also produce the flame and odour of a paraffin.
Polyketone is not the only candidate as a polymer made of C, H, O. Alcohol and ether functions too would at least account the number of O and H from the reactants.