The transaction history, and thus the ballance of an address is held in the blockchain, in the ether.
To spend the coins, you must have at hand:
* the current blockchain
* the private key
* a connection to the network.
What is considered risky is spending only a fraction of the paper wallet, for the following reasons:
- you just used the private key for creating a transaction, so the chances of it being compromised increases
- the client you used might have sent the change to another address while you're thinking the remaining coins are still in the paper wallet
But if it's done well, yes, it's possible to spend a fraction of a paper wallet.