Decarboxylation product of bicyclic compound
${\beta}$-keto acids typically decarboxylate very smoothly at temperatures between 100-200°C. The mechanism involves a cyclic, 6-membered transition state that first produces an enol intermediate (see figure). 



However in the case of your bicyclo[2.2.1] ${\beta}$-keto acid, a bridgehead double bond would result.  As you correctly point out, such a structure would be very high energy.  Therefore this compound does not decarboxylate at normal temperatures (reference, see p. 218, scheme 6.53).

I'm sure if you heated it hot enough something would happen.  It may decarboxylate via a free radical mechanism. The resultant bridgehead free radical could fragment or dimerize.  Alternately, and my preferred guess, would have the starting compound, in equilibrium with its non-bridgehead enol tautomer, undergo a reverse Diels-Alder reaction as pictured above.