(How) can a reaction be both stereoselective and stereospecific?

From what I have learnt, stereospecific and stereoselective reactions are defined as follows -


**Stereospecific** - The stereochemistry of the reactant dictates the stereochemistry of the product. Thus, an optically pure compound yields only **one** product.  

Examples - SN2 mechanism which leads to complete inversion of stereochemistry, bromination of alkene which always proceeds via *anti*-addition (hence, a *cis*-alkene will yield two enantiomers with the $\ce{Br}$ groups on opposite sides).


**Stereoselective** - The reaction yields **two** (or more) products, out of which one is major and others are minor.  

Examples - elimination reactions yield a mixture of *cis* and *trans* products, but the *trans* product is generally formed in a greater amount.


It seems to me that a reaction can either be stereospecific (yielding only one product) **OR** stereoselective (yielding >1 products with one in greater yield) and hence can't be both. However, my teacher recently told that some reactions are both stereospecific and stereoselective (and things being online, it'll be some time before she answers my query regarding her statement). I've also seen the same thing appear in some test papers that I solve. Answers to [this related question](https://chemistry.stackexchange.com/questions/72694/selectivity-in-organic-reactions) also seem to indicate that stereospecific reactions are a subset of stereoselective. I cannot understand how that is possible. Any insight would be appreciated.


