The scenario is: you’ve managed to receive ₩500,000,000 (~$337,265) at a Korean lottery (the catch is, only given in cash) which is delivered to you in two duffel bags. However will there be issues when returning back to the USA with that amount of money since it’s bundles of cash via foreign currency when the cap is $10,000 for undeclared amounts?
The 10k cap is not a limit of what you can bring in. You can bring in more as long as you declare it. Obviously you’ll be questioned and probably be investigated, but if the money is clean and legal, you’ll probably just have to pay taxes on it.