Nothing going into the desktop Trash Can?
How to fix my trash can
What do I need to restore my trash can?
MacBook Pro 13", OS X 10.11
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in the case of emails, they go into a trash folder inside Mail. Only when you "Erase deleted items" in that mailbox are they removed, and they do not exit via the trashcan on your Mac, they are removed directly.
The reason it is done this way is complicated. Readers can explain more, but only if you are interested.