[oh8eleven]

emails are never resident on a desk top machine.
Not true. I use Thunderbird email and during setup I selected "load new emails automatically onto my PC."
TB also gives me the option (during setup) to delete or save the emails on the host server.

[SampleMan]

TB also gives me the option (during setup) to delete or save the emails on the host server.

The point is that they are on the server UNLESS you delete them from the server.