Overall, nirvāṇa is a cessation and cessations are not existent entities, so I would argue the fact that nirvāṇa lacks existence goes without saying. Then there is also the undeniable point that only conditioned entities exist, and if you assert that nirvāṇa exists, you are by default stating it is conditioned, which contradicts the teachings given that we both know nirvāṇa is unconditioned. But to unpack this further for the purposes of discussion, here is Nāgārjuna offering insight into the position Madhyamaka takes on the matter:
- This pair, saṃsāra and nirvāṇa, does not exist.
Thorough knowledge of saṃsāra is said to be nirvāṇa.
- At the level of the unborn, there is no distinction of attaining nirvāṇa or not attaining nirvāṇa.
The unborn nature itself is also not there, because there is no thing which is unborn.
Madhyamaka dialectics are quite clear that an unconditioned nature is not established at all due to the fact that the alleged ultimate nature, is truly nothing more than the non-arising of the so-called "relative", and therefore is nothing in and of itself. That is the meaning of the emptiness of essence [prakṛtisūnyatā] and naturelessness [niḥsvabhāva], which are synonymous principles that that Madhyamaka undoubtedly champions.
Again from Nāgārjuna:
- Since arising, abiding and perishing are not established,
the conditioned is not established;
since the conditioned is never established,
how can the unconditioned be established?
Candrakīrti again echoing these sentiments:
- Since nirvāṇa is the supreme goal, it is the ultimate, beyond all suffering. This being empty of itself is the voidness of the ultimate. Indeed to counter the conviction that nirvāṇa is a real existent entity, the knower of the ultimate set forth the voidness of the ultimate.
The Mahāprajñāpāramitā-śāstra unpacks this principle of prakṛtisūnyatā a bit further:
- People still say: "The five aggregates [skandha], the twelve bases of consciousness [āyatana] and the eighteen elements [dhātu] are all empty. Only suchness [tathatā], the fundamental element [dharmadhātu], the highest culminating point of the truth [bhūtakoṭi] are true essences [bhūtaprakṛti]." - In order to cut through this error, the Buddha simply replied "The five aggregates [skandha], but also suchness, the fundamental element and the culminating point of the truth are empty." This is called the emptiness of the essences [prakṛtisūnyatā].
And then the tantras and various adepts of Vajrayāna, along with Yogācāra texts such as the Saṃdhinirmocana are brutally explicit in their clarification that nirvāṇa (and an unconditioned nature in general) lacks existence. They truly leave no room for misinterpretation.