In order to leave a hospital in Korea, you will have to pay your bill in full either with cash, a debit card, or a credit card. I'm not exactly sure if that's legal since it would seem to me that they're demanding a ransom to let you go home. But just be warned that people have started GoFundMe accounts precisely for this reason.
Let's assume that you can and will pay in full but they still don't want to let you or your child leave. Let's also assume that you or your child don't have any medical issues and they're simply keeping you because of hospital protocol. If you or your child is legitimately sick and need to be in the hospital, don't expect any of the choices below to work. However, you have a few choices if everything is fine.
1. The easiest thing to do is to just stay. Wait until they discharge you and then go home. Some places don't want to discharge people on weekends since the accounting department isn't fully staffed. (It doesn't make sense to me either, they should just be able to plug numbers in). What they might do is tell you they will overcharge you and let you go home on the weekend and then you're supposed to come back on Monday and they will fix your bill.
2. Don't ask for permission to leave, instead, inform them that you're leaving. This is what I would ideally do. I remember asking if I could leave and was told no. The next day, first thing in the morning, I informed them that I was leaving that day. It took four hours, but they finally discharged us.
3. Make threats. I wouldn't resort to this unless absolutely necessary, but if you're fine and can pay and they're still refusing to let you leave, then tell them that you will call your embassy and tell them that they're holding you hostage. Full disclosure, I've never done this nor do I know anyone who has, but hopefully the threat will be enough. I would tell them you're contacting the embassy over the police, because honestly, I highly doubt the police would do anything.
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