When we get this question, it is usually because the suspended attorney suspects that there will be unreported malpractice claims made against the attorney in the future. Generally when a malpractice insurer learns about the suspension, the insurer will either set the malpractice policy up for non-renewal or cancel the coverage immediately with notice. In either case the suspended attorney needs to act promptly to protect past acts coverage.
The suspended attorney is no longer licensed to practice law. The attorney malpractice insurance policy covers the work of a licensed attorney. It a matter of public policy that insurers cannot write insurance coverage where there is no exposure. As the suspended attorney cannot practice law, the policy will not provide any ongoing coverage for acts done by the attorney while suspended.
With a lawyers professional liability insurance policy being a claims-made policy, this leads to the question about how to cover past acts. The claims-made policy form generally gives to the insured the right to purchase an Extended Reporting Period Endorsement (ERP/Tail). The ERP then provides coverage for past acts. Problem is that many attorney malpractice policies take away that right via exclusion for attorneys that have been suspended from practice. With this exclusion, the only alternative for the suspended solo attorney is to make sure that they report any issues that they suspect might rise to the level of a claim prior to the termination of coverage.
To my knowledge there are no insurers that will knowingly provide coverage for a suspended attorneys past acts.