I am not working for DKB and any opinion I have is based on my own experience and the T&C of DKB.
The card carrier should have noted a "Verfügungsrahmen" which is your credit limit (if you got one).
In addition to your credit limit you can also do transactions that take your "Guthaben" (or credit balance) into account.
According to the T&C you are liable for 50€ damage for transactions that are made on the card before you notify the bank of the theft / compromise of the card. Once you notify them you are not liable anymore.
This is if you were doing everything right with your card, if you however did things like note the PIN on the Card, participated in the theft and other careless actions than your are fully liable.
If you have a credit on the card and your cancel the card DKB will transfer your credit over to your new card.
Now if there is a fraudulent charge on your card the bank will revert it and there is no difference if the card was in credit or debit. As long you have taken care of your duty of care with the card the bank will simply revert the transaction. There are time frames in which you must notify the bank of unauthorised charges.
But note you must inform your bank asap if there is something wrong and if your card is stolen/compromised you must inform the local police. They need a police report for stolen cards.
German bank T&C does not make a difference between a card in credit or debit, both are protected the same.
But again, I don't think DKB will be too hapy if you use the card as savings account as they only make money when you use the card.