The descendants will be the people living in Iran, Afghanistan and Central Asia. The Parthian Empire was an Iranian empire founded by the Arsacid Dynasty, who originated from an Iranian tribe native to the region of Khorasan (an area connecting Iran, Afghanistan and Turkmenistan). Iranian is an identity covering many Iranian peoples, the most commonly known being the Persians. However, there's many Iranian peoples with different cultures and dialects that are mutually intelligible on varying levels.
Khorasan was very prosperous and populated at the time of the Parthian Empire, and remained so during successive empires. It was heavily depopulated on separate occasions from Turkic and Mongol invasions, which started many centuries later. During these invasions, some cities were put the sword, and infrastructure like the extensive canal systems (which provided farming irrigation for the region) were consequently neglected and were slowly destroyed. The region of Khorasan is now a mix of Iranian and the Asiatic migrations the came afterwards.