Bond strength isn't just about the interaction of the two fragments bonded together. It is also influenced by the stability of those two species on their own. When the bond is broken, what pieces are left over?
The formation of radicals may be driven by the weakness of a particular bond. In terms of radical formation via bond homolysis, the reaction is more product-favoured if the bond being broken is weak. In other words, the bond is not very low in energy, so the overall reaction may become more downhill (or at least less uphill). In that case, forward reaction is favoured because of reactant destabilization.
However, a downhill reaction could also occur through product stabilization.
We have seen that the stability of anions and cations is strongly influenced by delocalization. Factors that spread the excess charge onto multiple atoms, rather than allowing charge to concentrate on one atom, make charged species much more stable.
For example, carbon-based anions are relatively unstable, but a delocalized carbanion is within the realm of possibility. Enolate ions are particularly easy to obtain because negative charge is partially delocalized onto a more electronegative oxygen atom.
Delocalization also strongly stabilizes radicals. It is one of the most important factors in the stability of carbon-based radicals.
Illustrate the resonance stabilization in the following radicals
a) allyl, CH2CHCH2 b) benzyl, CH2C6H5 c) cyclopentadienyl, C5H5