There might not be precise measurement system which bills you by the byte, but many provides monitor (or periodically sample) bandwidth utilization, so and using too much data will catch someone's attention.
Example from Hetzer, which claims to provide "unlimited" traffic. https://lowendtalk.com/discussion/180504/hetzner-traffic-use...
> We will routinely check your traffic use. If we continue to see such a high amount, we may choose to cancel your contract.