Last working date not confirmed after 30days since resignation

Hi, I put down my papers on 12th Nov 2015...prior that I had a discussion with my manager on 9th Nov 2015. As per my appointment letter, I am supposed to serve 30 days notice period. But, during my notice period due to viral infection I had to take emergency leave of 8 days. So, considering that my current employer is saying that 18th Dec 2015 is my official last working date. But, my new employer wanted me to join on 16th Dec 2015 and hence, I requested my current employer to sell out my notice period to me and relieve me on 15th Dec 2015. But, my HR replied to me that "it is not possible to relieve you from your duties tomorrow as he (my manager) has to review the KT document and gather the confidence, which is scheduled to be completed before 18th Dec i.e. official end date of notice period. Selling out the notice period would have been an option only if the reasoning are different from the above mentioned" So, my question here is - Whatever my HR told me is legally true? Can my current employer hold me even after completion of my 30 days notice period which is on 18th Dec 2015, saying that they are not satisfied with KT and has no confidence that new joinee can take up the responsibility? Also, if I decided to not to continue post 18th Dec 2015, can they deny to give me my relieving letter? Also, please note that I sent my resignation mail on 12th Nov 2015...since then I am constantly following up with both my HR and management...but, they did not reply to any of my mail till 14th Dec 2015 (more than a month) this case, if they try to hold me...can I file a case against them?