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They're still around although they are a minority now. However, they're decline correlates with the spread of Islam.
Iran was the center of Zoroastrianism so when Islam took Iran, a new state religion came to provide another major influence on the people. Of course they didn't all convert at once and dump their old faith somewhere else but gradually they went towards Islam instead with the increased presence of Muslims in Iran and the neighboring territories. In the Abbasid times especially, I've heard that there was a large movement towards spreading Islam to the people.
So people eventually became more attuned to Islam and Islamic culture than Zoroastrianism and its culture and it mostly fell away. Though i doubt persecution was significant early on, it probably rose with the passing of rulers and certain rulers who were worse than others such as the governor AL-Hajjaj bin Yusuf. That subdued the faith in region of origin while also making some of its adherents migrate to other places such as India.
I hope this addressed your question.
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