I agree with Ms (Cite Contribution), but you must inform the same to his/her family immediately whenever you found this problem because in this kind of situation people most of time can be found in two situations that we cant deny actually. The very first is that one can be damn serious and commit suicide anytime, which can be dangerous to both the parties. Second, this employee is just acting to take benefits, therefore, what HR Manager has to do is to take this situation very wisely.
First step, The Manager has to take him/her easy by saying that they gonna get him/her another chance of few more days to perform which he/she has to accept. Because the employee who threatens always expect quick answer by the Manager/Employer, which is really important and complicated situation for both the parties.
Second, Manager needs to assign this job to get him/her ease by any colleague/friend of this employee, so that, the immediate situation can be handle or control, and Manager/Employer can get time to take further and corrective actions. (Also suggested by Ms. (Cite Contribution) above)
Third, Manager must arrange a counselor for this employee and inform the same to the family of this employee. However, sometime employer/Manager feels that this action can make employee more impulsive and affect negatively but because in any case, employee took action, the employer can be found accountable for the situation.
Like Ms (Cite Contribution) said above “You can only offer balance and stability” these three quick steps can help Manager to handle the situation wisely.