Assessable Policy
  
Assessable policies allow the insurer (that is, the insurance company) to return the policy to the purchaser if there is a claim made that exhausts the insurer's reserves. In other words, if they can't cover it, they reserve the right to ask the policyholder to pay more than originally agreed.
This type of policy is usually only found with mutual funds. A mutual fund is a group of businesses and individuals that pool together resources to provide insurance for members. Obviously, this group would be smaller, and have less available to settle claims, than a traditional large insurance company. Non-assessable policies are the more traditional version. These policies require the insurance company to find the funds elsewhere if their reserves won't cover it (like selling assets).