Hello Marco,
yes, the options show up in the listings on the profile if you have BuddyPress or UsersWP installed and have set the “My Listings” link to direct there. If that setting is unchecked, then there is a special template page for “My Listings” where the links will show up.
The links increase load time, so they are not shown everywhere.
You have probably got it managed, but I will just point it out anyways that there is the setting in GD > General to either move Deleted listings to the trash or completely delete them. That setting is specifically to give you options to do something like recover a listing that an author deletes, and then change the owner/author if you choose.
Thanks for writing in with your question and feel free to open a new topic if you have more questions