If you swipe the wallet, then spend the outputs here's what happens:
YOU:
1) you import the private key from the paper wallet.
2) you create a transaction to spend the outputs associated with that key.
3) you sign your transaction and send it to whatever node / nodes you are connected to.
4) every node you are connected to sends your transaction to every node they are connected to.
5) very soon a miner sees your tx and scoops it up into whatever block it is mining.
6) various miners around the world do this till miner who finds the magic nonce does so with your block.
7) this miner then submits his nonce (with your tx) and you now have 1 confirmation.
Now IFF right after you swipe your wallet, and walk out, someone picks up the wallet and trys to spend it, the following happens.
OTHER:
1) someone imports the private key from the paper wallet they saw you discard.
2) someone creates a transaction to spend the outputs associated with that key.
3) someone signs thier transaction and sends it to whatever node / nodes they are connected to.
4) every node they are connected to sends your transaction to every node they are connected to.
5) very soon a miner sees thier tx and scoops it up into whatever block it is mining.
6) various miners around the world do this till miner who finds the magic nonce does so with your block.
7) this miner then submits his nonce (with someones tx) and you now have been robbed.
Whoever gets to #7 first gets the money.
So just be all James Bond and burn the paper wallet after you spend