Product Liability is an occurrence-based wording. This means the insurance needs to be in place at the time the incident/injury/damage occurred for there to be a valid claim. Professional Indemnity Insurance is a Claims Made wording. This means an insurance policy needs to be in place at the time you provide the service and at the time of the claim and/or incident in order for your interest to be protected.
If you cancel your insurance today and an incident is notified and/or occurs tomorrow for a product or service you provided last week, you will not be covered. Read more on this here.