This is the exact same thing that happened in Iraq after the first Gulf War back in 1991.

The northern part of the country, defacto-ruled by the Kurds had their own version of the Iraqi dinar, known as the Swiss dinar, as it had been printed by a Swiss bank note printer.

Due to the sanctions the central Iraqi government had to resort to locally printed bank notes of poorer quality for new notes. However, these notes couldn't reach Iraqi Kurdistan which had a fixed money supply. The Swiss dinar was soon worth 150 of the new Iraqi dinars.

Both of these have since been demonetized and replaced with a unified Iraqi-dinar, after the toppling of Saddam's government.