Unless rings are large enough (Bredt’s Rule), At small bicyclic bridgehead positions, planarity is difficult to attain, in other words, bridgehead carbon cannot have a pure “p” orbital. Hence,
- Bridgehead free radicals are pyramidal.
- Bridgehead carbocations are not possible.
- At bridgehead carbons, the double bond is not possible.
Unlike I, II (being a bridgehead olefin) does not exist. II has excessive steric strain as the rigid cage structure prevents the bridgehead carbon from being planar (flatten out). Bridgehead carbon can only have a “hybrid” orbital which, therefore, does not overlap well with an adjacent “p” orbital”.
As the bridge gets longer (as in III), flexibility return to the system and such bridgehead alkenes or carbocations may exist.
Decarboxylation of beta-keto acid involves both the free acid as well as the carboxylate anion. Carboxylate anion decarboxylates via a resonance stabilized enolate anion (stabilized by electron withdrawal).
Decarboxylation of free beta-keto acid involves six-membered chelated transition state and proceeds from keto to enol form of the product and in the final step, the enolic intermediate undergoes ketonization.
Bridgehead beta-keto carboxylic acids do not decarboxylate as it would require formation of a double bond at bridgehead carbon (in enolic or enolate intermediate) which would be highly strained.
You may refer- Organic Reaction Mechanisms