So I understand the initial Claisen. But the second step is the addition of an acid. Why wouldn't the resulting ester hydrolyze, giving you a carboxylic acid beta to a ketone, which would decarboxylate?
Because you first hydrolyze the ester with base, the protonate acetate anion with acid. Once you generate a Beta keto acid, it can be decarboxylated by adding heat. Only bet ketoacids ( acids on the beta carbon) can be decarboxylated with heat. Hope this helps.