Answer:
You can get disability coverage after a disability under certain conditions. It depends upon the cause of your disability and how long you have been recovered. Each carrier has different underwriting standards.
Some insurers will offer a guaranteed issue to employer groups. Your ability to get coverage will depend upon the required percentage of eligible employees electing coverage.
Obtaining private disability insurance after sustaining a disability may be more tricky, because disability insurance is medically underwritten. From the insurer's perspective, it does not have the same "law of large numbers" with an individual policy (because only one person is insured), as it does in a group disability policy. In most cases, the initial disability will be ridered (meaning that there will be no coverage for it, and perhaps, related causes).