Since cut fruit are held at low temperatures, further ripening is retarded.  However, there may be some softening and other changes but these will simply occur more slowly than they would during the ripening process at warmer temperatures.

Generally we consider that fruit have to be “near eating ripe” when cut and that there are few changes afterwards in the fresh-cut product.   Therefore you should have some specifications regarding the stage of ripeness you want from your supplier.  Usually this is based on a firmness measurement. 

Please note that there can be some variation on the specific requirements depending upon the particular product.
                                          --Marita Cantwell