How do I change the Apple Account on an old iPhone to a valid email address?

You cannot change the Apple Account unless you can access it first.

Is the Apple account that was not accessible, or just the associated email account?

Unless you had the Apple account deleted, or disabled, it should still be accessible weather or not the associated email address is still functional or not or even it does not exist.

If the Apple Account was deleted entirely by Apple, you can no longer use the device still linked to it. Apple warns of this when deleting accounts.

click here ➜ How to delete your Apple Account - Apple Support

• Make sure that you sign out of all your devices to avoid issues with apps that use your Apple Account or iCloud. After your account is deleted, you can’t sign out of iCloud or turn off Find My iPhone Activation Lock on your devices. If you forget to sign out, you might not be able to use your device when your account is deleted.

If it's just de-activated the Apple account, you can re-activate it again and log in as long as you have the Alphanumeric code that was issued to you when you had the account deactivated.

click here ➜ How to deactivate your Apple Account - Apple Support

If the iPhone is activation locked to an old apple account of yours that you cannot access anymore and you are the original owner and can provide valid proof of purchase Information  you can start an Activation Lock support request.