Termination may not preclude EAP use. Acts of violence and severe violations of organizational policies or work rules may be cause for terminating an employee. However, termination does not preclude you from reminding the employee about the EAP, unless policy does not permit use of the program by former employees. Although there is less incentive for a terminated employee to participate, it is a smart move to offer support and it can pay off in reduced exposure to behavioral risk.
Back up and start over. Supervisors may be reluctant to refer a troubled employee to the EAP when ongoing conduct and performance problems have led to a decision to terminate employment. Making a referral for the first time now may feel like an impediment to your goal of resolving the employee's problems through dismissal. It is a decision you should consider in consultation with your own advisors.
It's the best final chance. If you have not attempted an EAP referral before, you may feel no desire to try now. It may feel like you are offering "another" final chance. Ironically, however, the likelihood that your employee will make the changes you desire are now greater than before. This is because the threat of job loss is not just a possibility but a certainty. Making the offer is the next step, and later you will be certain that you made every opportunity available to your employee if termination ultimately is necessary.