Yes, there were once Jews living in Pakistan. I met one yesterday.
Fritha, whose family was encouraged with others of the Bnei Israel community to move to Karachi by the British - they needed their linguistic skills and trade contacts - attended a British school. At its height the community in Pakistan numbered almost 1,000. Life was comfortable. They had servants, but social interaction with all Muslims, save those who had lived in East Africa, was minimal. Fritha never visited a Muslim home.
A few Jews stayed on after the 1947 Partition and the massive wartime population exchange between Muslims and Hindus. It was in 1964, when Fritha was 12, that persecution finally drove the family to flee Karachi for India, leaving all their possessions behind. They were allowed to take just one rug with them. Frita's mother sewed gold coins into the lining. The women left wearing saris weighed down with coins. Once in India the family managed to survive by converting the coins into cash.
The Jewish Agency then arranged for them to make aliya to Israel, where the Jews were welcomed and helped to find jobs and housing. Many Bnei Israel Jews, who speak good English, found work at Ben Gurion airport.
Fritha recalls that the neighbours were a family of Turkish Jews whose daughters had flame-red hair. They had no idea that there existed dark-skinned Jews from Pakistan, anymore than the Pakistani Jews knew that there were Jews from Turkey with red hair. Despite the language barrier, the two mothers found they had plenty in common - and spent hours discussing how to handle their teenage daughters.