He sent me a link from IIT Delhi and IIT Bombay. Both IITs allow this. Any instructor in either of these IITs could inform its Continuing Education cell that s/he has no objection to allowing people from outside to sit in the class. They could be working in industry, or in another academic institution, own a company, or whatever. But they do want the person to have adequate background to be able to do the course. If the instructors permit then those courses are thrown open for public on payment of specified fee. Sometimes, if a course is popular, they may even change the timing to evening classes to enable more outsiders to attend the course. At the end of the course, the non-degree student gets a certificate specifying the grade received. This is one way the Institute can help people in the neighborhood.
Of course, IIT Kanpur offers short term courses for industry folks. These courses are typically 2-10 days compressed courses. And all IITs offer them. The goal for compressed courses is that people from outside the city can come for a short duration and upgrade the skills. But there can only be a few of them. By allowing people within Kanpur to sit through its regular courses, the options to local people become more by two orders of magnitude.
Even new IITs like IIT Gandhinagar allow this.
When I talked to a few faculty members about it, the immediate response is - there is no demand for such a thing in Kanpur. May be there is very little. May be this person who contacted me is the only one in the city who is interested. What is wrong in allowing such a thing anyway. (And based on my experience with IITK, I know that if tomorrow there is a lot of demand, we will not start it because there is too much demand and we can't meet that demand. Our quality of education for our own students will go down.) And I do believe that there will be several people in Kanpur who would want to do courses at IITK. For example, many of the project staff, who have done bachelors from poorer quality colleges would want to do a couple of courses "officially" where they have a certificate at the end. And we have a couple of hundreds of them at any point in time.
It is things like these where leadership can play a very important role. Since the perception is that there is hardly any demand, most faculty members would neither do anything to make it happen, nor would oppose this, if the Dean or Continuing Education Coordinator were to propose this.