Most states, including New York, have specific protocols for an insurance company to cancel a homeowner policy.
Homeowner insurance can be cancelled for non-payment of premium on relatively short notice; however, the mortgagee must be notified in advance. It is unlikely the mortgagee will allow the policy to terminate, especially if it holds escrow funds for premium payment.
Most mortgagees maintain property insurance to protect its interest on otherwise uninsured properties. Of course, this premium will be added to the uninsured mortgage balance.
In New York, the insurance company can non-renew a policy for underwriting reasons or cancel for cause mid-term with notice to interested parties, such as the mortgagee.
Underwriting reasons might be company oriented, for example, the company is no longer writing coverage in New York. Or perhaps the company no longer writes coverage within fifty miles of the coast.
Cancellation for cause is rarer. The company will non-renew for too many claims; but cancel for cause if illegal activity is discovered, or a fraudulent application was submitted.
The short answer, however, is yes, property insurance can be cancelled regardless of a mortgage lien. The lender must be properly notified in writing in order to have the opportunity to protect its asset. The owner must be notified in writing and given the time frame appropriate to the reason for cancellation to replace coverage.