In the onslaught of the Arab armies, Persian Empire collapsed. What do you mean by collapse? Defeat of field armies and their destruction, civilian areas open for Arabs to occupy. All this is fine. What happens to the armies? Either they surrender or they are annihilated. Surrender can be absolute, but annihilation? Is it possible? And it’s not as if there is a single battle. Battle after battle, defeat after defeat, retreat after retreat, after crushed rebellions, they finally wilted away from existence. Even a wilted flower still has a dried up stalk. Meaning, the remnants of the Persian army and Persian culture existed(Iran still maintains some of them). Not all commanders were killed or captured or surrendered – some retired and some shifted bases. And it’s not as if a commander escaped – he took some soldiers with him. An enclave with a different culture, but with formal patronage, it gets gradually assimilated into the local culture – new traditions, subtle modifications to way of life. Again, we need to look at this from two different angles – Withdrawal of armies – in this case, there is nothing but assimilation because of the small size, high mortality rate and literally no reproduction.
Withdrawal of citizens from the war zone – either they form a separate enclave, which assimilates much slowly and possibly never. The Parsi population is one which never assimilated. The percolation into China is something which got assimilated.
Now, the question is this. After the gradual collapse of Persian Empire, where and all did the soldiers go? And where and all did the people go? It is possible that if the soldiers are retreating through popular areas, people follow them. A quick glance of the map, you have the Byzantines, the Shahis and Kashmir, the Turkic Empires, Chalukyas, China and Tibet as the possible contenders. We know for sure that the Persian Crown Prince withdrew into China and he being the brother-in-law(or son-in-law?) of the Chinese Emperor, his family assimilated into the Chinese nobility. Kabul was raided for the first time by the Arabs when they were chasing Peroz. There was a military pact between Byzantines and Persians to bring down the Arabs and it collapsed because of jealousies and incompetencies. Turks, I am not sure because the Chinese were breathing down their necks and Persians were blood relatives. But, may be, they helped at a later date when held out Zoroastrian or used the retreating Persians as mercenaries or simply gave them refuge.
From being one of the greatest religion in the world, Zoroastrianism collapsed in no time. To look whether it survived if not independently, but as a part of some other religion, especially outside core Iran, should be an important topic to deal about – do we have the names of prominent Persian Generals in Byzantine or Chinese chronicles? And do we have any Persian customs in any of the bordering areas? The information will always be there – it’s just that we need to look at it at the same time. A simple example is Nowroz which is a state holiday from Kosovo to Mongolia.