Anybody born in Canada, even if their parents are illegally in the country, is automatically a Canadian citizen and has the right to reside in the country. The children's Canadian citizenship is not cancelled if the parents, who are illegally in Canada, are deported and take their Canadian-born children with them. I believe that the Canadia-born children who are overseas have to confirm their Canadian citizenship (children's and not the government's choice) when they reach a certain age.
Singapore arrests man who tried to join ISIS (Reuters)
from the article: Yishai: Deporting foreign children preserves Israel's Jewish identity