Dear Floating Penguin!
What does your question title mean? Do sleep forever or die - means the same right?
Neither do you wish to continue with the company anymore, nor do you wish to reveal to you next (fortunate) employer about this work experience, then why do you think that the current company must pay you?
Do you think that HR professionals are here to help you with crooked solutions, so that you can cheat your employer what so ever?
Even if you say your employer was not good, or cheated you, this need not be a reason why you are trying to be equally bad.
Stop sleeping, wake up. If such an attitude is conitinued, I am not sure how many companies you will be quitting in future.
And the answer to your actual question is here - check with your company policies, ask your HR where lies the maximum chance of getting more money - is it in getting terminated or resigning by self. Your company HR will definitely orient you once again.
Dont ever think that your future employer will never find about your past experience. Such things dont remain uner the cover for long. If you inform them that you moved out, since you felt that BPO was not your cup of tea - they will definitely understand.
Else, if they find it by themselves - thinsg will turn bitter for you.
Dont try to find which is the easiest route - always try to find, which is the right route. Take care, no offense meant.