QGIS 2.14.6 Processing Extension, 'Polygonize' Tool missing

As the Processing plugin has become core, you don't need the .qgis2/ version anymore.

In the recent QGIS version, the plugin can be found in (for example, in QGIS 2.16.1 standalone):

C:/Program Files/QGIS 2.16.1/apps/qgis/python/plugins/processing

So not only it is safe to delete the .qgis2/ version, it may be advised as it could help avoid conflict with the core version.