No trash and spam are not indexed by default. They are by definition garbage, not communications filed for your future reference so further disk space is not wasted indexing the garbage. I suggest you find another method of storing old mail other than the trash folder unless you want a catastrophic failure at some point. I can not speak specifically to the policies of "some hosting company" but it is normal practice with IMAP mail for the provider to routinely delete trash and spam folder content on a timed basis (usually around 14 days for spam and 30 days for trash). Providers that implement changes to their existing retention policies in this area rarely consult the user base before they act. When your mail provider deletes everything in the trash folder on the server, based on their retention policies, the IMAP account in Thunderbird will likewise synchronize the status change and delete the mail. That is how IMAP works, and as IMAP is the default I would expect you are probably using it.

However you can right click any folder and in properties set it to be polled for new message and indexed or not as you choose.

This specific scenario and change to default processing is covered in the support article here https://support.mozilla.org/en-US/kb/global-search#w_searching-for-spam-and-deleted-messages

As per this article:

https://support.mozilla.org/en-US/kb/global-search

Searching for spam and deleted messages

Trash and Spam folders are not searched by default. You may override this behavior for individual folders:

   Right-click such a folder.
   Click Properties in the context menu that opens.
   Check the box next to "Include messages in this folder in Global Search results."
   Click OK.

No trash and spam are not indexed by default. They are by definition garbage, not communications filed for your future reference so further disk space is not wasted indexing the garbage.

Hmm, I'll have to google again to find the Mozilla page that said otherwise. It explicitly said *all* folders are indexed by default. Since that's not the case that page should be changed.

I suggest you find another method of storing old mail other than the trash folder unless you want a catastrophic failure at some point. I can not speak specifically to the policies of "some hosting company" but it is normal practice with IMAP mail for the provider to routinely delete trash and spam folder content on a timed basis (usually around 14 days for spam and 30 days for trash). Providers that implement changes to their existing retention policies in this area rarely consult the user base before they act. When your mail provider deletes everything in the trash folder on the server, based on their retention policies, the IMAP account in Thunderbird will likewise synchronize the status change and delete the mail. That is how IMAP works, and as IMAP is the default I would expect you are probably using it.

You are correct that my email host, like most, has a policy of routinely deleting messages out of the trash. However, I have an "archive" folder structure set up in my email host account (which is set to never delete), and I have Thunderbird configured to use that folder as the "trash," such that I can simply hit the delete key and send a message from the inbox to that archive folder.

So my archive folder is not the trash according to my host; just according to Thunderbird, so that when I "trash" a message in Thunderbird, it always goes to archives.

Try pressing A to archive and let the garbage be garbage.

Your modified settings to turn the archive into trash is a significant part of this issue. I do wonder how stuff deleted into the archive manages to retain it's folder structure and year per the archive options. My feeling is you have lost all that functionality through your choice of archive key.

BTW Thunderbird will most likely not be syncing your archives to the server at all unless you open the appropriate folder. That is how the not checking of those two folders works, they are not polled for updates unless they are opened.