Messages kept being moved
Thunderbird keeps moving messages to other mailboxes. In one account it's spam on other it's Unwanted (I have both Unwanted and spam in both accounts,, though!). All moved messages have a common e-mail address in it; either as a sender address or a cc:. Both my e-mail accounts are on different servers. When I down Thunderbird no messages will be moved around until I open it again. I've done, twice, clean re-install of Thunderbird; I've manually removed all the files and directories associated with including my profile. Using different e-mail clients will not cause moving those e-mail messages.
Wšě wotmołwy (3)
Neither "spam" nor "unwanted" is a standard Thunderbird folder. I get the impression (correct me if I'm wrong) that you have consciously set up either of these folders yourself.
Spam. If it's really called "Spam" (and not "Junk") then it was put there by someone else; you, your av/security software or your email provider. Whilst Thunderbird can be set to use a "Spam" folder in place of "Junk", it's not likely to have happened by accident.
Unwanted. Again, this is not a regular Thunderbird folder and so we should ask who put it there and who manages what goes into it. Since Thunderbird itself won't set up this folder, (but maybe you did?) any automated movement of messages into it must be managed by either a filter or by some external agency.
The fact that you have these irregular folders suggests strongly that both accounts use IMAP, not POP. And if so, that means the folders in Thunderbird are reflecting folders on the servers.
In both cases, I think the respective mail providers are more likely to be behind this.
Wot Zenos změnjeny
"When I down Thunderbird no messages will be moved around until I open it again." So now I'musing webmail to access both accounts. NO message is being moved around. It'd be very strange that two, completely unrelated servers, under two separate admin do almost the same.
Webmail doesn't necessarily use the same set of folders, or the same folder names as we see via IMAP. "Unwanted" could be a feature to filter out message that you might not want to waste time and bandwidth downloading to a portable device.