How to identify the repeating unit in a polymer?
It's not that the "double bond breaks," it's that the vinyl C=C bond reacts during the radical addition polymerization to create polyvinyl acetate.

I'd disagree that the repeat unit is $\ce{CH3OCO}$ since that ignores the backbone entirely. Instead, if you look at the Wikipedia article (or any other picture of polyvinyl acetate), I'd call the repeat unit something like $\ce{-(CH2CH(OC=OCH3)-)}$ or something like that.