It's a neat idea, but if you sign up for a service and just cancel the card rather than canceling under the terms of the contract, can't the company still legal

It's a neat idea, but if you sign up for a service and just cancel the card rather than canceling under the terms of the contract, can't the company still legally attempt to collect on the payment if they want to? I suppose most 10-20/month fees wouldn't bother to collect, but they might pester you a bit with automated emails.