This is why counterfeit money is so bad - it's literally forging a debt of the government that never existed (essentially forging the government's name on a contract that says "I promise to pay the holder of this note $1" when they never did).
Anytime a dollar bill is inadvertently destroyed, this is equivalent to the creditor forgiving the government's debt. This is a form of seigniorage[0][1].
The USD is the currency of choice for many black market transactions across the world. These transactions are usually conducted in cash, and the cash is oftentimes stockpiled (kept in cash instead of deposited into banks) or used for other black market transactions. In many cases, very little (if any) makes its way back into the domestic legal market.
"Free loan" is a little hyperbolic, but it's a way of saying that the US has a number of overseas creditors who are unlikely to either demand that the US make good on its debt or sell that debt to someone who will. It increases the demand for USD internationally, which allows the US to print more USD[2] without any (or most) of the normal consequences of issuing debt.
There's a body of academic literature that goes into the impact of black market transactions on monetary policy. I'm running out the door so I can't look for it, but if you're interested it should be easy to find (though a lot of it may be paywalled by JSTOR and the like).
[0] https://en.wikipedia.org/wiki/Seignorage
[2] Sidenote, but this is why protests in which people burn dollar bills (OccupyWallStreet was one, though there are others) are so ironic - they're simply giving free money to the government, which is someties the exact opposite of what they are trying to convey with the protest.
[2] Here I use the term "print" both figuratively and literally, unlike before
As it is, it is a debt to repay $1 for each $1 bill. You might well ask, $1 of what? Since the government doesn't produce anything, it is a strange kind of debt.
$1 of tax-forgiveness is one answer. $1 of whatever our citizens produce is another answer. This 2nd answer is the reason why the demise of the dollar as the world currency (aka wealth reserve function) could lead to hyperinflation in the USA as all those foreign-held dollars come flooding back, looking for something domestic to buy.
As long as the dollar is legal tender within the USA, foreign "creditors" (in the sense used in the above comments) can always get something back (however debased in value).
If like Brazil and Argentina, the USA defaults and creates a new currency (it'll never happen, right?) then good luck to all the drug-dealers of the world trying to cash in their old greenbacks.
<edit: phrasing!>
