Has anyone heard of, or better yet sold, a "backup primary" GL...

Has anyone heard of, or better yet sold, a "backup primary" GL policy? Not an excess, but a second primary in case of failure for the first/main primary? We have an animal shelter getting moved to non-admitted, and they are interested in a "backup primary" policy to replace the state guarantee fund they'd be losing from leaving admitted markets. Is this a thing? Has anyone heard of, or better yet sold, a "backup primary" GL policy? Not an excess, but a second primary in case of