It'll likely only cover the cost of the building and public liabilities, not the contents and probably not much in the way of injury/death coverage (if any).Doesn't the insurance of the building's owners cover such things as fire and injury to tenants?
Usually contents and life cover are left to the tenants although they may be able to sue if it's shown the building owner was negligent (so several years down the line).
Even if it covers more it could be months/years before it's paid out if there is any question of blame.
