= Solution
<hydroxide> attacks an <ester> <carbonyl> to form a <tetrahedral intermediate>. Collapse expels ethoxide, and <acid (chemistry)>–<base (chemistry)> transfer gives the <carboxylate> and <ethanol>. Repeating this <nucleophilic acyl substitution> at the other <ester> produces the <malonate> dianion; <acid (chemistry)> workup gives $\mathrm{HO_2C{-}C(L)_2{-}CO_2H}$, with $L=\mathrm{CH_2CH{=}CH_2}$ as defined above.
On heating, one <carboxylic acid> group is lost through a six-membered cyclic <proton>-transfer/bond-cleavage arrangement. A <carbonyl> <oxygen> of the retained group accepts the <proton> from the departing carboxyl OH as its C–C bond breaks and <carbon dioxide> forms; <electron> redistribution gives the <enol>-like form of the retained <acid (chemistry)>. <proton transfer>/<tautomerization> then produces
$$
\boxed{E=\mathrm{HO_2C{-}CH(L)_2}}.
$$
The net <decarboxylation> is $\mathrm{C_9H_{12}O_4\to C_8H_{12}O_2+CO_2}$. The central <carbon> gains a <hydrogen>, both allyl <substituents> survive, and only one carboxyl group is removed. It would be incorrect to draw <hydrolysis> directly giving the final <acid (chemistry)> without accounting for this <carbon> loss. The favourable cyclic pathway is characteristic of <malonic acid decarboxylation>.
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