Google-drive – What happens when I delete a Google folder or document (or PDF) owned by someone else

Giving edit access to Google Drive documents is sufficient. The way these files work, once they are shared with a user, the file will appear in their "Shared with me" list

If they remove or delete a file from this list, it will not remove the document from any other user's list, nor will it destroy the file. Only the owner can trash a document.

Learn more about trashing documents here: http://support.google.com/drive/bin/answer.py?hl=en&answer=2494934&p=restore_trash_collab

If the owner trashes a document, they can get it back from their Trash folder:

Learn how to recover a file or folder that you moved to the trash.

If something in Google Drive is moved to the trash, you'll see a warning and you may lose access to it at any time. Read one of the following sections to learn how to restore it to your Google Drive from the trash. When you restore something, it'll be recovered in Google Drive on the web, to the Google Drive folder on your computer, and to your mobile devices.

If the item is in a folder, you’ll need to restore the entire folder to recover any individual items inside of it.

Owners

If you're the owner of something and you’ve placed it in the trash, you'll see a warning that reads "This item is in your trash" when you open the doc or file.

If you’d like to restore a doc or file to your Google Drive:

Search for it in the Trash. Select the file(s) or doc(s) you’d like to recover. Click the Restore button.

Folders and file structures behave the same way, if regular editors remove these it will disappear from their "Shared with me" list but it only affects them, not the rest of the collaborators.

From a comment by Maxim:

Currently (2016.08), if I share a folder with another person, all files inside this folder get shared as well, but not the subfolders. In other words, Google Docs sharing it is not recursive, indeed, (though not in the way @Fibonacci described this).