As has been stated, the transaction of the bitcoins is held in the public ledger that is the bitcoin blockchain. You can see this online, or keep a copy on your own computer and the bitcoin-qt client will alert you when a transaction on the blockchain includes one of your bitcoin addresses.



If there are no miners, the blockchain will not get updated with new transactions, so bitcoins can't be spent as the new transaction will not be included on the blockchain (the blockchain is not being updated).