No, Cobra does not include disability insurance or life insurance. Cobra is just for health insurance and possibly dental insurance, flex spending plans, and other health related benefits.
If there is an individual disability policy, it can be taken to the next job. Otherwise, the employee will need to wait until the next job to see if they offer group disability insurance, or purchase a new private disability insurance policy at that time.
No, COBRA does not include any benefits other than health insurance. The Consolidated Omnibus Budget Reconciliation Act was passed by congress back in 1985 to insure employees moving from job to job didn't lose their health insurance coverage in case of a major or long term illness or accident that was currently being treated. No other benefits including disability nor life insurance was included in this law.
If there is an individual disability policy, it can be taken to the next job. Otherwise, the employee will need to wait until the next job to see if they offer group disability insurance, or purchase a new private disability insurance policy at that time.