In drug design, how does the incorporation of halogen increase its stability?

The most typical reason why halogens (esp F) are incorporated into drug candidate molecules (usually replacing a proton on an aromatic ring, for example) has to do with metabolism. Oxidation of compounds is one pathway by which the body begins metabolizing drug substances; hydrogens are frequently one spot where oxidation occurs. In replacing key protons with halogens, that oxidation pathway is generally shut down -- allowing the original drug substance to survive longer as such in the body, and therefore have longer period of time to have the desired clinical effect.

there could be free radicals (substances lacking one electron) in those drugs, and since halogens have 7 valence electrons, they would react with the free radicals, taking the latter's extra electrons with them