Does this issue only occur if you have billing info on file?

I'm using the free tier and have no billing info set. According to this https://github.com/netlify/ask-netlify/issues/6#issuecomment... > if you have an event that puts you over the free-tier limits, Netlify will ask you to update your billing information and add a CC

Although worryingly > We just had this happen and our site didn't stop working.

Is there any way to ensure if you hit the limit sites just stop working and you don't get billed?