When may the commissioner examine the affairs of an eligible unauthorized insurer?

The correct choice indicates that the commissioner has the authority to examine the affairs of an eligible unauthorized insurer when deemed necessary and at the expense of the insurer. This reflects the regulatory framework that allows the commissioner to ensure that all insurance entities, including those considered unauthorized, comply with the necessary regulations and maintain the financial integrity required to protect policyholders.

This power is essential for maintaining oversight over insurers that may not be subject to the full range of regulations applied to authorized insurers. By allowing examinations when deemed necessary, it provides flexibility to the commissioner to investigate potential issues as they arise, rather than being bound by specific conditions, thus supporting the overarching goal of consumer protection.

The other options suggest limitations or specific circumstances under which an examination could occur, which do not align with the broader authority granted to the commissioner in overseeing the industry's compliance and operational standards. This way, the system can respond dynamically to changes in the insurer's situation without unnecessary delays.