This is an excellent question, not the least because it is extremely complicated and politicized, but also because most of the scholarship behind it has been politically charged.

Before we can discuss what exactly happened to China's currency, it is only natural that we should talk about China's currency. Unlike the main powers at the time, China's currency was essentially based off of the Mexican peso, or the Spanish dollar, the silver coin that had dominated Pacific trade for centuries, and had been one of the most dominant currencies throughout much of early modern Chinese history. It was a precious metal in addition to being used as currency, so it was felt that even in times of crisis that the coins would retain value due to their dual nature as both currency and commodity.

During the 1910s and 1920s, China had seen one major revolution, followed by a transitional period that later led to the government being toppled and a variety of warlords fighting each other in internecine warfare. One such group was the Kuomintang, who-having originally cobbled together the Republic of China government in the first place-was one of the more powerful groups. This culminated in the Northern Expedition, where Chiang Kai-Shek, the leader of the KMT, essentially defeated most of his active rivals and was able to take over the government. He had many opponents, including internal KMT dissenters in the left-wing, the Communists, and some of the other warlords that he had not suppressed, but essentially he had secured control of China, abet at tremendous financial cost.

Then the Great Depression happened.

The Great Depression did not, as the conventional wisdom would assume, impact China directly. China's markets at this time were still fairly isolated from the more integrated global economy, so there was little initial damage done. What soon happened though was that several nations loosened or got rid of their precious-metal linked currencies. Britain cancelled its gold standard, and the US restricted private ownership and exchange of gold as a direct backing to each note. This naturally drove the price of these precious metals-now wholly commoditized-up. For countries like China, which had a lot of precious metal currency, this was a massive speculating opportunity. Many speculators sold their silver coins in exchange for US dollars and British pounds and other such currencies. However, this rapidly drained China's currency reserves, as the same silver coins that were sold off as a commodity were also the same silver coins used for daily consumption and business. Essentially the life blood of China's economy was being leaked out, paralyzing investment and consumption, leading to an utter collapse of the economy.

After several poorly handled attempts to mitigate this, the KMT government decided to seize control of the banks and institute a fiat currency in an attempt to stop the outflow of silver and to restore the ability for people to do business. However, there was little confidence in this fiat currency, and the imminent outbreak of the Sino-Japanese War in 1937 caused the government to print large amounts of currency that created a good amount of economic chaos.

While during the war the US eventually helped to prop up the Chinese currency via supporting it with US currency, in the immediate aftermath of the war the US aid was curtailed and the hyperinflation-which was already happening regardless-ramped up considerably. The inability of the government to properly fund its armies or to purchase equipment and supplies resulted in the utter collapse of what little logistical capability the KMT had to begin with, and a wave of subsequent Communist military victories was the result.

Sources:

Shiroyama, Tomoko. China During the Great Depression: Market, State, and the World Economy 1929-1937.

China White Paper, Department of State, 1949