It's similar with power/water bills. They can't/won't cut utilities, a form of subscription with a fixed cost in addition to the usage cost, right away (there is a process for that), but you owe the money all the way until they are cut.
But that’s kind of beside the point. When you sign up for a subscription, they only commitment you have made is for the chosen billing interval.
If it’s a month you’ve committed for a month, if three years then you’ve committed for three years.
But you have not in any way shape or form committed to a single second beyond that.
Most (all?) have auto renewals clauses that are very convenient for both the seller and buyer, but to enforce it when the buyer wants to quit is basically extortion.
"If you do not timely cancel your subscription, your subscription will be renewed at the price in effect at the time of the newel, without any additional action by you, and you authorize us to charge your payment method for these amounts...We do not refund or credit for partially used used billing periods."
This can be easily read and argued as: if you do not cancel, you owe them. You can argue this in front of a judge, but it will be really hard to say it's "extortion" if the cancellation process is streamlined.
But the basic reality is that none of these firms would enter into a contract with terms like these because they are outrageous.
Just think about it. The act of doing nothing over a certain short time period is supposed to legally bind you in a new contract and even with unknown pricing?
This is not business between equals and people behaving this way deserve all the crap they can be tossed.
I don't do yearly subscriptions for this very reason, though.
It is entirely possible to sign up for a paid-monthly perpetual subscription that is much harder to cancel than "Just stop paying".
Gyms are kind of famous for doing this.
If Netflix chooses to cancel or pause the subscription after the gift card runs out of funds, that’s their business decision. It’s probably wise as a practical matter for them to limit access to unpaid services when it won’t usually be worth their time and money to force the matter judicially.
But other things they could choose to do include continuing the subscription and using any and all legal debt collection methods until you catch up on the accrued debt, imposing reasonable penalties for nonpayment as per any specific contract wording or any applicable legal defaults, and claiming any damages and/or lawyer fees incurred depending the specific circumstances and the rules of the relevant legal jurisdiction.
The details do vary between countries and between some countries’ subdivisions, sure. But the general principles of what I’m saying are typically true in most countries.