Halogenation has been one of the most used strategies to explore the reactivity of empty carbon cages. In particular, the higher reactivity of non-IPR fullerenes, i.e., those fullerenes that do not satisfy the isolated pentagon rule (IPR), has been used to functionalize and capture these less stable fullerenes. Here, we have explored the stability of the non-IPR isomer C72(11188) with C2v symmetry, which is topologically linked to the only IPR isomer of C70, as well as its reactivity to chlorination. DFT calculations and Car-Parrinello molecular dynamics simulations suggest that chlorination takes places initially in nonspecific sites, once carbon cages are formed. When the temperature in the arc reactor decreases sufficiently, Cl atoms are trapped on the fullerene surface, migrating from not-so-favored positions to reach the most favored sites in the pentalene. We have also discussed why cage C2v-C72(11188) is found to take four chlorines, whereas cage C1-C74(14049) is observed to capture 10 of them, even though these two fullerenes are closely related by a simple C2 insertion.