Firstly, I would like to thank you all for your inputs. At first, I thought the information I had typed was enough to get answers from the experts, as I am posting it for the first time. Thanks to Mr. Lakshminarayanan for your answer.
Coming to Mr. Banerjee, thank you too, but the answer is still not clear even after I have explained it fully.
My New Offer
Here is my new offer - the employer is not forcing me to join immediately. Initially, they just asked whether I could join within a week. However, my current employer refused to relieve me within a week and asked me to complete a 2-month notice period.
Currently, I am serving the 2-month notice period, which will end on August 16th. As of today, they are saying that until a replacement is found, they cannot relieve me.
I am not thinking about pending salary, taking legal actions, or other measures at the moment. I just want to know what I can do if they do not relieve me on my last working day, stating they will not issue the relieving letter. The relieving letter is important to me, and I am continuously working on finding a replacement.