It's A Snowflake...shut Things!
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No best answer has yet been selected by ginger 69. Once a best answer has been selected, it will be shown here.
For more on marking an answer as the "Best Answer", please visit our FAQ.ginger 69, it IS possible to become overdrawn with an account offering a solo or electon debit card. I worked for a high street bank for 17 years, I know.
The card itself works by checking the available funds in your account, so as long as the funds are available at the time of the transaction, it is authorised. However, inbetween the transaction being authorised and it actually debiting your account, a cheque or direct debit could be presented. It would be returned of course, as there were no funds, but most banks can and do charge for unpaid cheques/direct debits. The card payment is guaranteed so this would take you overdrawn straight away. Most / a lot of accounts that only offer debit cards like solo or visa electron do offer cheque books or direct debit facilities.
Other senarios exist wherby an overdraft could arise on such an account, although it is unlikely, it is still possible.