Currently serving notice period. 1.5 months into a 3-month notice period.

Requested to encash leaves and management's initial response was will look into this and revert. Dragged for a whole month, gave them the push and was finally informed they can't encash. The short of it is they're forcing me use my ALs to leave earlier.

Need to clarify two things. Annual leaves are paid, right? But also, employers aren't legally obligated to answer to any requests for leave encashment per labor law.

Did the math and realized I'm losing out 4k-ish. Not a lot compared to most job seekers here, but that amount amounts to ~25-35% spending power and hoping to secure it. Question I have in mind is, if the management refuses to encash, can I simply just extend my notice period by the AL count to justify getting paid? Frankly speaking, I have no need to use these ALs to off early nor go anywhere. Yes, I'm aware I'm still doing extra work and losing out on the paid value of my ALs, what else can I do? Or do I really just let the 4k go?

Have you gotten a new job? If so, probably can negotiate with new company to start new job earlier. But legally can or not, is another thing to consider.
Even if you extend notice period, it might still be the same if the new company doesn’t allow double employment as above.
You might earn a bit more if you negotiate earlier start date with new company assuming higher salary there, and if new company have policy of prorated bonus and increment next year, you might earn a bit more as well.

all depends on company HR policy lo

Short answer to that question is a no. Not sure if the initial title was unclear, but company in the title refers to current employers.

The long story is I was placed on PIP and decided to leave mid-PIP to avoid further complications and have been serving notice since then. Following pro-rata, I have unused ALs which my current employers are forcing me to take in lieu of encashment, though I'm keen to capitalize on the payment for reasons stated in the original post. Hence asking for workarounds.

PIP is a difficult thing for both employer and employee. Sorry to say I understand why the employer doesn’t allow the encashment in this case. Try to negotiate the end date again with the employer, or clearing your leave first before the last day, perhaps it make you feel better that you are not doing anything during that few days but you still getting salary paid.

All the best.

Best to take the AL and start to search jobs asap..
There is no rule that says company has to pay you cash for unused AL.