I kinda doubt they immigrated there. The family could have lived there for many, many generations, even 1,000s of years. Under the Shah life was very tolerable even if they did not have absoulte religious freedom. Khomeini promised religious tolerance when he came to power.
Just picking up and moving to another country when things go bad is not always easy - as even a number of FReepers are now finding out. But it's true that they had the option of emigrating to Israel, as does every Jew.
One could leave but with only the clothes on their back. Any equity or wealth would probably have to remain.