The first consideration is whether the wellness program is a stand-alone plan or if it is bundled with the medical plan? In other words, if an employee waives the medical plan, can they still participate in the wellness program? If they can, then it is likely a stand-alone plan.
A stand-alone wellness program will most likely be subject to COBRA and ERISA on its own if it provides medical care. The concept of medical care is based on Section 213(d) of the IRC and generally includes physical examinations, health screenings, and treatments (such as a flu shot). The program would need a plan document and terminated employees with a triggering event would be offered the opportunity to continue participation in the wellness program through COBRA. Participation would be on the same terms and conditions for similarly situated active employees, which would include incentives and rewards such as gift cards, etc. So, while one may suppose that having a standalone wellness plan (providing medical care) would alleviate COBRA considerations, it actually creates more work for an employer plan sponsor because the stand-alone wellness plan would have to comply on its own with COBRA, ERISA, etc.
If the program is integrated with the medical plan, then the COBRA and ERISA requirements could be met by the combined medical plan documents and communications. A COBRA beneficiary would elect or decline the wellness plan and medical plan together. If elected, the participant would receive the same incentives and rewards as the similarly situated active employees as discussed above (including gift cards, prizes, etc.). They would also be entitled to the premium discounts.
In summary, an employee who is continuing participation in the wellness plan through COBRA would receive the same coverage (and rewards) as an active participant. If it was a stand-alone plan (providing medical care), then the wellness plan would be available through a separate COBRA election. If it is bundled with the medical plan, then a COBRA election of the medical plan would mean the former employee COBRA participant was permitted to continue participation in the wellness program on the same terms as an active employee.