Well, the only way the foreign student can stay as you describe is through..........H1B
So an Indian fellow who studies four years at MIT can only get an IT job with an H1B visa? I find that hard to believe
There have always been students who remainined in this country legally-before H1B visas even existed. This program is not needed except for very rare cases where a certain expertise is needed. I think I’ve seen one or two case like that in my entire working life.