Strong Base combined with Sp2 carbons in Nucleophilic Substitution and Beta-Elimination Reactions
The strong base is capable of being a nucleophile in this sort of situation; deprotonating tert-butyl alcohol will increase its nucleophilicity. In an SN1 reaction the overall rate is only dependent on the loss of a leaving group, so a strong base/poor nucleophile will react via SN1 as long as there are not plausible E1 pathways (e.g. sp3 bonded hydrogen alpha to carbocation).