Not all SN1 reactions are created equally.
There are two possible outcomes here, one leading to solvent separated ion pairs (high probability of epimerization or racemization) and the other leading to a contact ion pair, where things get strange sometimes. In contrast to the solvent separated ion pair, a contact ion pair derived from a chiral compound IS chiral.
The contact ion pair SN1 proceeds via a mechanism "in between the SN1 and SN2." The carbocation is formed via first order kinetics, however the anion remains in close proximity to the cation, and varying degrees of the substitution may take place from the opposite face, leading to stereochemical inversion.
Please see March... Advanced Organic Chemistry, Stereochemistry of SN1 Reactions for a more comprehensive explanation.