How should I deal with such matter?

Hmmm correct me if I'm wrong but it seems like your helper is trying to avoid the medical checkup result? Am I reading between the lines properly or looking too much into it? Anyway, if I was in your shoes, I'd be okay with letting her go back but only after all the loose ends are tied up, in this case, the medical, the thumbprint and a replacement. Maybe you should also seek advice from the agency from which you hired her from, see if they can help. To me, if my helper has been with me for years and is trustworthy/loyal, I wouldn't mind letting her go home for a week but if she's new or you don't really have a good feeling about whether or not she's coming back, then maybe it's time to consider other options.

Maybe you can have a chat with her to find out what are her concerns? Whether or not she is having some family issues back home or is there some other issues (feeling overwhelmed?)? It could be that she is unclear of what is expected of her or perhaps she is having some difficulty? Sit her down to have a chat. If you think that she is capable and would like to keep her, see if you could make some adjustment to address her concerns. It could be that she is having some family issues and would need to settle that as well. You could also speak to your agent and let them find out what is the issue.

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Sounds like she wants out and doesn't know how to tell you. From my experience many helpers are prone to lying and not being direct even when asked. If I were you I would def look for a replacement

Oh.. it does sound like some excuses for some other issues. Did you find out from her previous employer why he/she did not continue with her? Good helpers are difficult to find. Good luck!!