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That's right.
I once ran a university branch and a colleague I was friends with lied to the person I had left in charge because I was on vacation.

When I got back to work and was told about it I called the management and after analyzing the situation I just told her that I had lost confidence in her. Two days later she left work.
Maybe she understood the seriousness of what she had done and decided to leave.

The wrong people tend to cull themselves meaning they tend to move away of their own accord.