SEOUL—When the coronavirus ripped across South Korea in mid-February, bar owner Seo Ji-won felt somewhat secure. He had some savings, didn’t have a family to feed and ran a popular establishment in a busy neighborhood.

Last week, Mr. Seo decided to close his 10-table business, called CTavern, for at least a month. Emergency funds earmarked for small establishments like his have yet to materialize. Even as South Korea’s coronavirus pandemic has eased, his bar remained nearly empty. Sales plummeted 90%.

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