Yes they are.
You can change insurers whilst a claim is still open, but that won't stop your original insurers dealing with the claim just because you've taken your business elsewhwere.
Let's say you had cause to make a claim on the very last day of your insurance policy (and we'll use car insurance as an example), because your car has caught fire and is not a burnt out shell.
You can't afford another car until you ghet paid out, so whilst you don't have insurance anywhere else, you no longer have insurance with your company.
Your insurer is still obliged to deal with the claim as the insurance was in force at the time of the incident.
Same principle applies if you insure elsewhere