Set up a not-for-profit organization is a good idea for getting a E-7 VISA in Korea, it's called a liaison office or representative office in Korea for a foreign investor who want to study for a market situation of Korea without capital injection.
This simple organization can't issue an invoice to earn or sales but still can hire employee, and join to the social security program and so on.
You can register this type of org. at the court if you had an entity in your country, but it's strictly prohibited for a sales activity.
This type of org. can't earn and sales something, so there is no tax liability but only for employee withholding tax return without corp.income tax return or VAT return responsibility.
A lot of foreign religious org. and you can set up this type of org. more easily from the beginning if you don't need a visa.
More details, please send me an email to firstname.lastname@example.org