When Thunderbird is closed, the program is not running and it is not connected to the internet. It is not possible to download.

If you are arriving and starting Thunderbird and emails are already there, without any connection to server, you could only test this if you preset Thunderbird to open in Offline state everytime. Then it cannot have access to internet on opening and should not be able to download, so would show no new emails since closing. Does Thunderbird auto open in offline mode ?

Are you talking about an imap or pop mail account?

If I discovered downloaded emails which I did not download, I would wonder who had booted up computer; used my User Account password to gain access and then started up Thunderbird in my absence.

I was pretty sure it wasn't hooked up to the net but I'm the first one in here in the morning and for the last three Tuesdays in a row the mail that arrived overnight was sitting in Thunderbird already. There's only one other person with a key and I asked if they have been accessing TB before I get here. The response was they don't even come in that early on Tuesday. It's not a big deal because it's just me using this system. It just seems weird that my mail is waiting in the inbox when I start TB. I'll try leaving it in offline mode before I shut down the program. Maybe I'm accidentally hitting a button when I wake up Windows. Thanks for the help!

It does it on two different servers, both are set up as POP.