I don't understand your question. If a base is promoting an E2 elimination of an alkyl halide, there is no bromine free radical produced. Bromide ion (bearing a negative charge) is produced. With respect to the size of a base, the size may influence which proton is removed, but in the E2 elimination, the proton must be alpha to the leaving group, meaning that it must be on an adjacent carbon. It might help to draw out the reaction in which you are interested.