Ask HN: Are email providers required to give email access if locked out?

For example, if Google/Yahoo/Microsoft or whomever, locked you out of your account for 'suspicious behavior', breaking TOS, or some other reason are they required (legally) to provide you with copies of your existing emails? Regardless of if you've actually done anything? This hasn't happened to me but I've heard horror stories about it happening to others. What are some mitigations that my not so tech savy grandmother could take to prevent this from happening?