Unfortunately, the current stimulus package, which offered extended and discounted COBRA insurance premiums is no longer available.  That means that you can only sign up for COBRA insurance for the typical term length of 18 months.  The only other way you could qualify for extended your benefits is if you have a second qualifying event like the the death of the covered employee, if the covered employee  starts receiving Medicare benefits,  or if there is a legal separation or divorce.  This also would only extend to the spouse or any dependents, not the covered employee themselves.