Carbocation Rearrangement in SNi
The Mechanism of the reaction
The reaction of an alcohol with thionyl chloride under base-free conditions is one of the most significant examples of the SNi mechanism (DN+ANDe to give it it’s correct IUPAC designation, which is perhaps more instructive in this case).
There are two steps to the SNi mechanism, as shown below (figure taken from Bruckner, Organic Mechanisms [1]):

Step 1: The alcohol reacts with thionyl chloride to afford an alkyl chlorosulfite, which can often be isolated.[2] At this stage, the oxymethine stereocentre hasn’t been touched– it’s the second step that will determine the stereochemistry.
Step 2: The chlorine is delivered intra-molecularly, with extrusion of sulfur dioxide gas. Since the sulfur is being delivered from the same face that the hydroxyl was on, the reaction occurs with retention overall.  This can be seen in the dotted lines in the figure above.
Two things are worth noting at this stage:

If pyridine is added to the reaction mixture, we see overall inversion via an SN2 mechanism.[2] This occurs because the pyridine interacts with the intermediate alkyl chlorosulfite formed, liberating a free chloride (nucleophilic) and hence allowing the substitution to take place  inter-molecularly. This can be seen in the solid lines in the figure above.

The second step in which I described as happening intra-molecularly doesn’t quite happen intra-molecularly. In reality, the C-O bond begins to fragment in an SN1 fashion, before the chloride attacks. The reason why we still see retention (rather than racemisation as is common with  SN1) is due to a phenomenon called contact ion pairs.[#]


Carbocation rearrangement
The simple answer to your question is that at no stage of the reaction is it thought that there is any free carbocation concentration, making rearrangement less likely on kinetic grounds (along with elimination, which could equally be argued by your logic).
The ion pair theory is such that the carbocation remains closely associated with the leaving group, allowing the nucleophilic attack to occur rapidly without the need for an additional collision to take place.
[1]: Bruckner, R. Organic Mechanisms- Reactions, Stereochemistry and Synthesis; Springer: Berlin, 2007
[2]: J. Am. Chem. Soc. 1952, 74, 308
[#]: You can read about this in any advanced organic chemistry text such as Carey or March, and is a bit too long of an explanation for me to give satisfactorily here