Yes, fiduciary liability insurance, as well as life insurance, disability, director's and officers, and employment practices liability insurance.
Yes, typically both ESOP's and EOT's should consider having fiduciary liability insurance, which can protect the company against potential lawsuits arising from the operation of the ESOP or EOT, such as claims of breach of fiduciary duty, misrepresentation, or improper management of the plan.
Other insurances to consider (and which would apply to worker co-ops) include life insurance, disability, director's and officers (often sold in tandem with fiduciary liability insurance), and employment practices liability insurance.