Until 2010 or so, foreigners were not allowed to represent national teams. That situation changed only 10-12 years ago, when the Emirates Cricket Board pressured the ICC to change the rules, with open support from the pig-3. And the gulf model has been adopted by the other countries as well. Out of the 105 ICC members, more than half (especially those in the gulf and the Europe) doesn't have a single citizen playing for them. And because of these nations, those teams playing with native players are losing out.
It is a news for me; I have not come across any article on the foreign player policy of ICC. If I remember correctly, I first saw Kevin Peterson was playing for England and Usman Khawaja for Australia after that lots of players migrated to New Zeeland, Australia and England.
In my opinion, the country which got the maximum benefits out of this foreign player policy must be England as they have won the 2019 WC with an Irish Skipper.
I have not seen India signed any foreign player so far but interestingly India head coach Rahul Dravid once played for Scotland; I was really surprised on hearing that but not getting any background information about that deal because as far I have been watching him since his debut in 1999, he was successful with India and led India for 2007 WC as well but not sure when he played for Scotland.