Stuck in Notice Period Limbo: How to Handle a Manager Who Won't Let You Leave?

I have served my 2 months' notice, and I'm on my 3rd month now, which is going to end by 5th Nov 2019, and then the fourth month starts. It is a startup, and they are getting new projects, but it is getting delayed day by day. Even two weeks before, they gave me a new project without taking my notice into consideration. When I bring up the issue, they tell me to finish the work and then leave.

My manager keeps insisting that I complete the projects, and new updates keep coming every day. He says he will only relieve me after all the work is done; otherwise, he suggests that I abscond. What should I do? Kindly help.

This is their reply to my notice period message sent to them three months ago via email:

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This is to confirm the acceptance of your resignation, and your last date of relieving would be 05/10/2019, considering the following factors below:
1) No bugs on any of the products you have worked on or are currently working on.
If bugs are found, you would be required to complete them before getting relieved, as discussed with the management.
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As per the offer letter issued by the company, it's clearly mentioned that the notice period and after completing the notice period, the company is bound to give relieving with completing all exit formalities.

Please send an email to your Senior HR, copying your supervisor, to confirm your relieving date and ensure you are released on time. Also, highlight the section of the notice period mentioned in your offer letter.

It is not clear if your notice period is 2 months or more. Please go through the terms and conditions of your appointment order and write to your Company HR that you are currently serving, quoting the relevant terms and conditions, clearly mentioning the date of resignation and completion of your notice period.

The other side of the coin is that, by virtue of your roles and responsibilities, your employer will expect you to finish the assigned tasks before you leave. It depends on your role. It is not that one can simply wash their hands of responsibilities by walking out just because the notice period has been completed as per employment terms, even though legally it is right.

However, in your case, since you are in the third month of your notice period, talk to your immediate superior and HR and explain your situation. Tell them politely that you are ready to support even after relieving to the possible limit. Please don't strain the relationship, especially during the relieving process. Talk to them and arrive at an amicable relieving date of mutual agreement.

You have not mentioned whether you have a new offer. If so, explain your situation to your current employer. If not, finish your assignments and get relieved.

The Last Working Day (LWD) in your case is 5-11-19. The terms and conditions expressed in your appointment letter apply, whether it is a 3-month notice period or payment in lieu of notice. Simply walk away at the closing hour of the stipulated date with prior intimation.