Geez, no? Sanctions work only if the sanctioning entity has power. If the US govt sanctions you, they can tell all banks in the world that if they touch your (virtual) money they'll be sanctioned too. If some podunk dictatorship no one did business with announced "Any bank doing business with xxpor will be barred from working in our country!" then many banks will probably say "Fine, you're a tiny economy that we don't have anyone that does business with a business in your country anyway, so you can take that sanctions and shove it".
Ironically paper money is the way to "escape" sanctions, because anyone around the world knows that that 100 dollar bill can be exchanged for goods and services. And it doesn't even have to involve a bank, just another person who recognizes the value of that paper, in a chain of transactions. Depending on the hassle you may need to pay more..
If I bring a suitcase full of dollars home with me from a trip to the US (assuming I make it through border control with that much cash), I don't see what kind of jurisdiction the USA would have over me for simply owning dollars.
These are just pieces of paper, they don't provide any kind of jurisdiction. The American banking system may refuse to serve me perhaps, but it's not the dollars that give the American government any control. Hell, several countries outdid e the USA use American dollars as an official currency, but that doesn't make them vassal states to the USA.
Your local bank won't protect you from the American judicial system. If they get a court order they'll just fork over your assets. Your bank wants to maintain it's ability to exchange funds with American banks. The American banking system will refuse to serve your bank if they refuse to comply. Or more like they'll just order JP Morgan or whomever to fork over your bank's cash because that's how banks interact with each other.
If you got a pile of dollars in the US, you did business in the US and if that business has any tenuous connection to what the courts are after you about, we have jurisdiction.
If you don't like it you have to run to China, Russia, Iran, etc.
> which entity gives those pieces of paper their value
The USA can print and lend dollars to control the value of the currency on the global marketplace. When trading outside of the USA, people give the bills their value.
You can substitute a suitcase with a million dollars for a suitcase full of gold or a suitcase full of diamonds, or a suitcase full of Pokémon cards. Outside the official banking system, the value of paper money is whatever the people trading perceive it to be. In some cases, that value can be larger than a million dollars (i.e. in countries where their own currency is in a free-fall, where the government is trying to limit the supply of foreign currency, but people want to exchange their local currency for something more stable; people in Argentina, Lebanon, Sri Lanka, and Turkey might want to do that).
If, for whatever reason, Russia pays for North Korean drones to murder Ukrainians, there's absolutely nothing the American government can do about that.
The US and most of the world may recognise those pieces of paper as worth some of their currency. This doesn't mean I can't recognise them as toilet paper.
Ironically paper money is the way to "escape" sanctions, because anyone around the world knows that that 100 dollar bill can be exchanged for goods and services. And it doesn't even have to involve a bank, just another person who recognizes the value of that paper, in a chain of transactions. Depending on the hassle you may need to pay more..