When the old execution plans changed in plan cache
The are a lot of caveats about execution plan generation and reuse, so the old saying 'it depends' definitely comes into play.  I think you will find some very valuable information from these links (they include examples of various tests):

https://www.brentozar.com/archive/2015/01/updating-statistics-cause-recompile-no-data-changed/

https://technet.microsoft.com/en-us/library/ms181055(v=sql.105).aspx

https://www.brentozar.com/archive/2013/12/recompile-hints-and-execution-plan-caching/