In the early Universe, the relative abundance of a massive weakly interacting particle species "freezes out" when the annihilation rate becomes less than the expansion rate. Although ineffective in reducing the total number of the species, occasional annihilations still occur after freeze-out. The residual annihilations of massive particles ($10 \mathrm{MeV}\lesssim m_X\lesssim 1 \mathrm{GeV}$) after primordial nucleosynthesis can strongly alter the light-element abundances through photodissociation. For particles with typical weak-interaction cross sections and lifetimes ${\tau }_X\gtrsim 5\times {10}^6$ sec, we find that the mass range $m_X\lesssim 1$ GeV is ruled out, independent of how they subsequently decay.

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