Firstly, management wants to understand the factors that have prompted him to resign and could try redressing it or taking corrective measures to avoid such circumstances in the future. Secondly, since he has resigned within a week's time, they feel that the employment opportunity given on a mutual growth perspective has been misused and thus are not willing to release his pay for the period he worked with us. Kindly advise on how to proceed further...
Honestly, getting feedback from our employees so that we can improve is a very nice idea. I support you for that. But have you heard of "There's a deal for everything."
Suppose I am that person who left the firm in a week's time. You are asking me to come to your office to discuss what made me resign in a week's time. Your motive is to get feedback from me so that you can try to rectify if there is an error at your end (i.e., the company is at fault) or if YOU (as in the management) THINK the matter is trivial, convince me to join you back.
Please note that if an employee has resigned, he would not be willing to come back to the company to meet you and give you feedback. He is not reachable on the call, proving this. Another thing, if he is coming down to meet you, you would get feedback, you may improve for the future - all this is your benefit. What about him? He would waste his precious time (which he may very well use to go and give somewhere an interview) so that you can benefit at his own personal loss which you don't even wish to consider?
As said by Tajsateesh sir, a few hundreds or a couple of thousands can't put a big hole in the pockets of the company. And if they are so concerned about the money flowing out, better drop the idea of chasing him and getting feedback. We cannot force anyone to work for us, neither can we kidnap someone and force them to open up and say what made them resign. When I resigned from my last employer, I said I wish to resign for a personal reason and though they tried to probe me to know the actual cause, I didn't share because I didn't trust that they'd relieve me if they got to know the truth. However, to me, relieving didn't matter much, since my new employer wasn't fussy about it. But I didn't want the absconding title and then fight to get the letter and other hassle.
If the company wants feedback, the company should consider the time and effort a person would put in to give one. And it is not necessary that you'd get an honest feedback when you are seeking one. But at least this gesture would give you positive word-of-mouth advertisement from him. Perhaps he didn't like the way things were working at your firm, but with this, he will have the benefit of doubt that perhaps the company was not fully at fault, there was some mismatch in the expectation and reality on his end as well.
Further, it is your decision completely. But in my opinion, if you are not planning to compensate him for the tenure he served, don't call him for the feedback also. Let him go and have his own life.