When you give in to threats from an employee, you can be assured of one outcome: there will be more threats in the future.
In a word, you should not give this employee a raise merely because she threatened to leave. By providing a raise under these circumstances, you are rewarding poor work and threats, and this will destroy any incentive for her to try to improve her performance. In addition, when other employees learn that poor work means nothing and raises are granted to those who threaten to leave, you can expect them to follow suit. If she is able to pressure you into giving her a raise, your entire raise program will be seen as a sham, and that would be a shame.
You have a raise policy that is based on merit, and you advised this employee of the actions to take if she wants to be eligible for a raise. For whatever reason, she did not keep up her side of the bargain. She should be eligible for a raise only if she improves her performance. And if her performance continues to be substandard, it is possible that the decision to leave will not be hers at all.
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