You have not stated which industry you are in and what your position is in the company.
The reaction of companies differs and there is no straight answer to give you. In most companies the fact that you have served notice period is enough for them to give you the reliving letter. However, if you have not done any work in the notice period, for whatever excuse you give, there are chances that the company will refuse to do it claiming that you have not done any work or completed a handover.
You can take legal recourse, but that is a long drawn process and in any case, they are going to give negatives in any background verification.
What you can do in the remaining week again depends on a variety of factors that we can't as ascertain since we haven't been in your company and don't know the attitude of the HR or managers.
Therefore, the best option for you would be to approach your manager and ask him what you need to do in the remaining week to complete the pending work that was a sign and how to complete your hand over properly. You should also speak to the HR and see what needs to be done the remaining period to get relieved properly