Looks like it got stuck in the rollers or the wheels. A top loader with 2 cards in each pocket with cardboard is too thick to make it through. Everyone I receive with cardboard in it is beat-up in some way. I never use cardboard because it has to bend or get beat-up and not once has anyone complained. I've even sent 3 cards in each pocket with 2 stamps. No problems the top loader bends just enough where the cards are not.
What I do is load the cards fold the top, down first then the bottom up. That way none of the openings are showing and the cards can't move. Fold a piece of paper around it, tape it closed, and write a thank you and the Id#. and away it goes.
It very easy, if it can't bend the envelope it has to be hand-sorted and you have to pay more for that.
At 1:07 to 1:27 on this video, you can see where it will all go wrong, if it can't bend. This is where your cards died. At that speed, they were torn & crushed. The machine stopped and what was left, was pulled out with pliers and dropped in the trash.
https://www.youtube.com/watch?v=4HpRMlhXm6I
The cardboard is doing nothing but increasing the odds of damage than doing more good and your paying more for it because it's more weight.
What is that behind you!?! Oh, It's me! Looking at the cards you have, That I want. :)