Can insolvent insurance companies participate in amnesty, similar to bankrupt entities?

Yes. An insurer that is under supervision, is currently in liquidation, or is under rehabilitation may be able to participate in the Amnesty Program.  For insurers under supervision, they will need the prior written approval of the Insurance Department or the appointed supervisor.  For insurers in liquidation or rehabilitation, including those under a Federal or state receivership, the liquidator, rehabilitator, or receiver acts in place of the insurer and so is responsible for participating in Amnesty on behalf of the insurer.