Pitch Continuity and Rests

Whether playing Haydn, Mozart, Beethoven, or Schubert on the piano apparent phrase endings indicated by slurs and by rests are often not really endings but rather deceptive suspensions of continuing resonance.  How often do these composers use exactly the same sonority on both sides of a rest or a phrasing indication?  Surely it is a matter of an interruption rather than an end and a fresh beginning.  This could only have occurred to them because of the relative ringing of the instrument when compared to the harpsichord or clavichord. 

Modern readers see a rest and they stop their ears.