As far a debit card not being declined, it depends on where you are trying to use it. For instance, if you are trying to withdraw funds from an ATM and the network is down, the machine is required to dispense the funds.
Additionally, many retailers have debit systems that allow you to swipe your card, but it does not instantly "freeze" the funds, nor withdraw them. In theory, you could use your card and go withdraw the money, causing it to bounce.
As far as going into the negative without overdraft protection - as you can see, it is possible. It is up to the financial institution to decide what they want to do, they can either "bounce" the check or they can allow the account to go into the negative - either way, they will likely charge overdraft fees.
Hope this helps
