I am more familiar with the Romanian situation, but African and Middle East countries with "Marxist" orientation used to sent engineers to follow specialization courses and students to study in communist Europe. This was part of an effort to avoid dependence upon the former masters of Western Europe during the process of post-colonial modernization. The visiting 'specialists' had no time to integrate the local society, as they stayed for months, weeks or even days. Students stayed for longer periods (years).
On the whole, in spite of the official discourse about socialist friendship, theses states were focused on maximizing control over their citizens, and change of residence or citizenship between socialists countries was totally discouraged.
As said by @Arved: European communist countries used to welcome university students from communist countries, and from countries that were aligned at some point with the communist block.
I know of students of Syria, Iraq, Algeria, Libya and Tunisia studying in Romania in fields like engineering (especially in oil production) and medicine — and, more surprisingly, even of an Ethiopian studying theology in Bucharest in the 1960s!
Students were coming for specific universities. I'm not familiar with Bulgarian universities. In Romania, the oil industry and medicine were the most sought-after. In Bulgaria it might have been shipping or some other industry.
Here is a map of the "socialist-leaning" states. (The presence of Portugal there is odd. The closer the geographical vicinity of a country, the greater the chance of having students from there).
But: all these were people coming for their university studies, not people living there, with high school children. Among these students, there were no Iranians I guess, in Bulgaria. (Before the Islamic revolution, the Persian regime was anti-communist. Ceausescu's Romania had at some point good relations with the Islamic republic: but that was exceptional and short, and sending students to an atheist country was improbable.)
Diplomats' children were not normally studying in local schools, but in special ones.
There were some communists from Greece emigrating to some countries (Bulgaria, Yugoslavia, Romania) after the military crackdown against communists there.
Considering people of black-African and Arab descent:
Again from my Romanian experience: there were some cases of male students from the aforementioned countries that had children with local women (usually colleagues). Most of these children never left. Maybe this situation could fit the OP's story.