Change region with money in account

You don't. You have to remove it first. See all the requirements in the article Change your Apple Account country or region - Apple Support.

There are TWO methods whereby you can empty balance. Method #1 is the simplest (you can do it yourself) and has the additional benefit that you get to use your money for something for yourself instead of donating it to Apple. In situations where you cannot contact Apple it may also be the only way you can empty the balance.

#1. If you still have a valid credit or debit card from your original country, you may purchase an item from the App or iTunes Stores for more than your balance. The remainder will be billed to your card, leaving you with nothing in your account balance. If Apple does not provide support in your old country, or you cannot contact Apple Support for your old country, this is the only solution for you.

#2. If you cannot do method #1, you can ask Apple Support to remove and keep the balance. Use https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0998&symptom_id=20198 or the contact link in the section “If you can’t spend the last of your Apple Account balance to make changes to your account” in this article --> Check your Apple Account balance - Apple Support . You may be able to get chat support.

Apple will keep the balance when using this method .

Alternatively give Apple a phone call. Find a list of telephone numbers at: Contact Apple Support - Apple Support . You will need to contact Support for the country to which your account is set, but the telephone numbers are not international, nor does Apple provide telephone support in all countries. For some countries look under “Other” listing at the end of the list.

If you can neither add a payment method nor contact Apple, your alternative is to create a new Apple Account. Avoid doing that if at all possible. It will cause a LOT of complications with your current content and could potentially also result in problems with using your hardware.