Plex doesn’t delete any files, unless it is instructed to do so.
It will delete files if the server admin (or a person who has access to a device that is signed in to the admin’s Plex account) deletes an item explicitly from within a Plex client: https://support.plex.tv/articles/202606363-how-do-i-delete-something-from-my-library/
It will also delete TV show episodes automatically, if the server admin has set the episode retention to anything other than the default settings, shown below:
If you are using a Synology NAS, verify that the media files have proper access permissions for Plex to be able to access them.
The upgrade from DSM 6 to DSM 7 brought major changes in this regard: Synology FAQ - Questions, Answers, and How-To's - #37 by ChuckPa
