Not sure if a bug or a feature, but I've recently started to pay closer attention to the cards that my dolls wield to battle, as I've became more interested to play with customisation, now that I have nearly every card available. It seems like whenever the day in Glitch City resets, my dolls also get their equipped cards swapped, instead of keeping what I gave them. I haven't tested it in detail, but just yesterday I had my bunny and puppy wear Hunter AI cards for Basher and Spammer, and as I entered today to check on bank affairs (last few days were terrible on EXE market) - they ended up wearing cards with no attributes, and those weren't even the same characters I equipped on them! Still not sure what happened there, I'll try to monitor it some more and report on any findings that might help to pinpoint the issue.
Update: The issue doesn't seem to be related to the Glitch City resets, but it's definitely there and it's a bit hard to say what exactly causes it. I still can't say for sure, but just today I've observed how instead of having equipped U001 +1 U002 +1 U002 +1 U023 +7 on my dolls from top to bottom, I ended up with U014 +0 U000 +0 U001 +1 U022 +2. There is no rhyme to it, and I can't clearly understand the reason to this happening. The only imaginable culprit would be the fact that yesterday the only thing that I've done was collect cards and money from prisoners, check all building NPCs, collect all bits on the city floor and leave without entering Tangent Twins building/fighting any battles. Might've even opened one of card packs. So my guess would be that equipped cards shifted within a save file during the process, meaning that equipment is tied to a slot of data within a save instead of item id. But that's just a wild guess, I still have no reliable way to reproduce the issue.