What happens to the bank and shop contents when the city is destroyed? do contents fall into enemy hands?

Here's what I've noticed, with my limited experience:
Each (melee) hit gets some stuff from inventory. Usually resources (gold, wood, stone, metal), and also I've gotten scroll and potions.
Each reduction or destroy of a building seems to get building materials (gold, wood, maybe stone) and house spirits. I haven't noticed getting anything that looked like building contents.
Hope this helps.

No, they do not.