There are some people, especially in the Western world, who view modern day India as an impoverished Third World country, an undesirable destination which supplies immigrants to other countries but does not attract immigrants in return. Now this is not exactly true - modern India has had longstanding problems with illegal immigrants entering its borders.1
But modern history aside, India has in fact attracted immigrants since ancient times. Jews from Western Asia first started arriving in India 2500 years ago.2 Zoroastrians from Persia came to India between the 8th to 10th centuries.3 Arab Muslims settled on the Indian coast in the late 7th century. The 13th-18th centuries saw the influx of Muslim immigrants from Central Asia, West Asia, and East Africa, many of whom were escaping political instability in their own countries.4
The late 4th century/early 5th century Chinese pilgrim Daozhen, who visitied India during its Golden Age, abandoned his plans to return to China and decided to live out his life in India instead. One reason given was that the monk Daozhen so admired the monastic discipline of Indian Buddhism that he preferred to continue his religious practice there.5 In another telling of how Daozhen decided to part ways with his companion Faxian, Daozhen was not just of the opinion that China did not compare favorably with India on the basis of Buddhist religious organization, he also held the view that India was politically more stable than the then-chaotic China.6 It appeared that Daozhen preferred to remain in India because he believed that he would have a better quality of life there. Faxian returned alone to China, bringing with him a number of Sanskrit scriptures. His travels would inspire later Chinese monks to make the pilgrimage to India.