She's a member of a bunch of groups, a lot in the Daegu specifically. I looked at one, KAPS: Daegu Dog Walking Club and checked out a few of the posts to see if she had liked, or commented on any. There's also a "seen" option.
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That post is from April 27th. The "having no friends" thing could be explained by having really high privacy settings, couldn't it? Maybe she does a lot on her fb, and we just can't see it. Or if it is a fake profile, the people are doing a good job of randomly making it seem active.
Here's a post she liked
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There's also a post that she shows up on "seen" from May 8th.