Hi there!
A specific example eludes me right now (though if I think of one, I'll post it!); but, generally speaking, for a reaction to be stereospecific, the reactant must first exist as a stereoisomer. Any reaction that starts with an achiral starting material, but produces a mixture of stereochemical products, of which one stereoisomer predominates, would be stereoselective but NOT stereospecific.
Hope this helps! I will keep digging for specific examples for you.
V