If the pollen grain of one flower lands on the stigma of another and they are of different kinds,i.e.they belong to different species then cross-pollination won't take place because the 2 flowers belong to different species.The pollen will fail to germinate and perish and no pollination will take place. It doesn't reach ovule. In shortshort until and unless the stigma of that flower receives pollen of its own species pollination won't take place.This is the natural process.