That varies from hosting provider to hosting provider.
Some will suspend your account if you go over your disk space limit or monthly quota, while others will let you off with a warning.
You should be aware, though, that some companies will charge you expensive overage fees for exceeding their limits. When that happens, you may have a nasty surprise waiting for you when you open next month’s bill.
When in doubt, you should always carefully read over the Terms of Service agreement, as well as any other legal agreements offered to you at signup.
If you see that you are about to go over your space or bandwidth limits, you should immediately contact your hosting provider and ask about upgrading to a plan with higher limits.