This sort of thing is technically possible for children of Indian citizens born in countries without birth citizenship, see e.g. https://en.wikipedia.org/wiki/Indian_nationality_law#Citizen.... Given that millions of Indians live in Persian gulf countries with these sorts of citizenship laws, I wonder if it has ever happened.
Statelessness absolutely does happen. On 13 November 2018, Filippo Grandi, United Nations High Commissioner for Refugees said there are about 12 million stateless people in the world.