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From a security standpoint, you shouldn’t click any links in email messages when it comes to finances, especially easy blue buttons to fix things. Instead check the validity of the message, with regards to the due date and other mentioned information. If it all seems plausible, then go to your accounts settings yourself, don’t click links in messages.
Avoid phishing emails, fake 'virus' alerts, phony support calls, and other scams - Apple Support
Identify legitimate emails from the App Store or iTunes Store - Apple Support
Update your account info safely
If you receive an email asking you to update your account or payment information, only do so in Settings directly on your iPhone, iPad, or iPod touch; in iTunes or the App Store on your Mac; or in iTunes on a PC.
To update your password for the Apple ID that you use for purchases, do so only in Settings on your device or at appleid.apple.com.
Learn more about security and your Apple ID.
With that being said, it is the user’s responsibility to have the funds ready on the due date. It is the user’s responsibility to know the due date. You can check the due date in your subscription settings.
Apple will cut you off from the service when the payments stop. You can resubscribe when you can afford it again. If the gap is short in days, then you can use the existing iCloud Music Library again. If the gap is too long (*), then your old iCloud Music Library will no longer exist.