There's a strictly finite value base - assets, economic output, etc - to all fiat money supply. It's the underlying value, things priced and transacted in the fiat currency, that make it valuable. You can easily spook the confidence in fiat by doing stupid things to an economy.
Otherwise Venezuela would be the richest country in world history right about now, given their inflation rate.
It works identical to mathematical halving in concept. Yes you can keep going, and no you'll never reach zero. However every time you debase the currency to pay for something beyond your budget, you destroy some of the value underpinning it. You make the assets and transactions in that currency less valuable. You can infinitely subdivide the currency, and each time you do it, you destroy more of the value base. Eventually you're splitting pennies, so to speak. This is especially true in cases where you're printing to pay for something you can't afford (almost always the reason for such printing), so what you're really doing is eating the nation's asset base through the currency debasement.
Just ask Japan, they sliced more than 1/3 off their standard of living by debasing the Yen over the past decade. They had no choice due to their debt situation (they needed to stealth default), however it reduces the value of the assets that are held in Yen, making it easier to eg use dollars (or gold) to buy those assets (whether businesses or real-estate and so on).
So sure, in theory can you infinitely print currency. In practical application, you destroy the value of the things that underpin the currency and the whole scheme self-destructs given enough time and 'printing.' That puts a more realistic cap on actual potential money supply. The fact is, it inherently must be finite. Eventually your money is not worth anything, as you destroy the assets under it. As that happens, people stop accepting the worthless currency, it becomes too expensive to 'print' it and support it, and it becomes a self correcting system, in all cases and without exception.