This will depend on individual bank policy.
Federal Reserve Regulation D is the regulation that requires banks to disallow more than 6 "convenient transactions" in a month on savings accounts. If they do allow it, they will fail their audits and be fined.
As a result, banks will do one of several things: either prevent you from any more transactions for the month, charge you a fee, convert your account to a checking account, or simply close the account altogether. If they do that, they will give you the money in it (probably by mailing you a check).
You have a few options before that happens. First of all, if this is an account that you regularly spend money out of, the appropriate account type is a checking account. You could go to the bank and open a checking account, which will not have a transaction limit.
If you are unable or unwilling to do that, you'll need to stay under this limit. However, you should be aware that not all withdrawal types fall under this "6 transaction" limit. The regulations talk about "convenient transactions," which generally include things like automated payments, debit card, check, internet transfers, etc. Cash withdrawals in person or at an ATM generally do not fall under this limit, so that is an option for you if you hit your limit for the month.