No, disability insurance cannot be "ported" as health/medical coverage can under COBRA. There is a risk to the insurance company that you could change occupations to something more dangerous or hazardous, or not work at all if you left your current employer.
Best to contact a local insurance professional to discuss your options.
Agent Owner, Gilmore Insurance Services, Marysville, Washington State
Can you Cobra disability insurance? No, not under current COBRA guidelines. However, depending on your plan at work, it may be portable without further health underwriting. In any work situation it is always a good idea when parting ways to go through all your previous benefits to find out what you can and can't do. It's actually a good idea to go through all the details of your plans when you become eligible for them. Unfortunately, most employee plan summaries look the same at the end of the plan as they did at the beginning.
Best to contact a local insurance professional to discuss your options.