There is no user fee for using equipment (except phone service which has nothing to do with Apple) or for using an Apple account. The previous owner probably had a subscription running. When you replaced that person's card with yours it just started charging yours instead of the previous owner's. This support article explains how to cancel a subscription from Apple on an Apple mobile device, Mac, PC, and online ➔ If you want to cancel a subscription from Apple - Apple Support
You may wish to note that what you are doing is, from my reading of it, against the terms of use of the account:
Legal - iCloud - Apple
IV. D. No Right of Survivorship
Except as allowed under Digital Legacy and unless otherwise required by law, you agree that your Account is non-transferable and that any rights to your Apple ID or content within your Account terminate upon your death. Upon receipt of a copy of a death certificate your Account may be terminated and all content within your Account deleted. Contact iCloud Support at iCloud - Official Apple Support for further assistance.
