This may be by design or I may be missing something, but it appears to me that assigned messages remain assigned when they are archived, but then when viewed on the archive list there is no indication that they are assigned until the message is opened. Also, the assigned messages list excludes assigned messages in the archive.
It seems to me that as long as the message is assigned to someone, it should always show up on messages lists and in that user’s assigned messages list.
It is by design that archived messages remain assigned. This allows you to track a message while waiting for a reply (which would unarchive it).
I’m confused about the rest of your concerns. PMs appear in my assigned list even when archived, and I see assigned indicators in the archived topic list:
Thanks. What you’re describing is what I would expect. I’m still wrapping my head around what is happening. Do you have any group messages that are archived and assigned to you? Are those showing correctly in your assigned list and showing the indication that they are assigned to someone?
Yup - I can confirm that on my site assigned messages appears to work correctly everywhere except when they are in a group archive. Once they land there, they disappear from the user’s assigned list and lose the indicator that they are assigned to someone.
Looking at your screenshots it appears that this is working correctly for you but here are screenshots showing it not working for me on my site. Puzzling. See below.
First message in this moderators group inbox is correctly indicating it is assigned to someone. When I look in her assigned list it is also present.
Then I archived the same message - see here in the moderators group archive it is not indicating it is assigned to someone. When I look in her assigned list it is not present.
(Also noticed another bug, perhaps reported elsewhere already and deemed minor, that when you click on the indictor that a message is assigned to someone it takes you to that user’s assigned topics, not messages.)
Not here on Meta. As shown in my screenshots, I can see a group PM I’m assigned to that’s archived in my assigned list, and I see assignments in the archive. I’ll look more tomorrow.
Hmm… what about PMs in group messages that are assigned to someone else and archived?
This is a real problem for me because I have been assigning alot of tasks to people in the moderators group and then archiving them, and then wondering why nobody is doing them. Gah! Any help appreciated in getting this fixed. 
Here’s the repro on my site as of this morning:
@tobiaseigen, can you check the value of the unassign on group archive site setting? Following your repro steps on the new site I just set up I still see assignments in my list when archived, and the assigned users are listed in the archive view:
