Does Nirvana have svabhava in Madhyamaka? As suggested in this comment, we shall try to look more closely into this.

Does Nirvana have svabhāva in Madhyamaka?

Here, svabhāva is as defined in Nagarjuna's Madhyamaka, and commonly translated as inherent existence, inherent nature or inherent substance.

Why conditioned things (the Pali term sankhara) do not have inherent existence (svabhāva) is explained in this answer, this answer, this answer and this essay.

However, Nirvana is unconditioned. So, does it have or not have svabhāva? And why?
According to Madhyamika, whatever is dependent-arising is empty of svabhāva. As Nagarjuna says, the meaning of emptiness is dependent-arising; and dependent-arising is the meaning of emptiness. Each and every phenomena, be it permanent or impermanent, form, consciousness or non-associated compositional factor, lacks svabhāva.

There is a number of reasons supporting emptiness of svabhāva. In his commentary to Gyaltsab Je on Maitreya’s Sublime Continuum, Geshe Gyaltsen said:


  There are specific reasonings to realize emptiness that are suitable
  for specific disciples, like the diamond slivers, the four
  possibilities, the king of reasoning that is the reasoning of
  dependent arising, and the reasoning of not being one or many.


In his commentary to Tsongkhapa's Special Insight Chapter of the Middle-Length Lam Rim, Geshe Gyaltsen explains dependent arising:


  Dependent arising means that phenomena depend on something else to
  exist.


On the fact that both samsara and nirvana are empty:


  The perfection of permanence [that is possessed by a buddha] refers to
  the equality of samsara and nirvana seeing both as empty of inherent
  existence.


All phenomena are dependent-arising. If it exists conventionally, it either a permanent or an impermanent phenomena. If it is a permanent phenomena, it does not depend on causes and conditions (the grossest level of dependent arising) but it still depends on other factors.

Even permanent phenomena such as space, emptiness (the absence of svabhāva), partial and complete cessations (such as nirvana that is the final true cessation) are dependent on part. Geshe Gyaltsen also says:


  Since the aggregates are impermanent phenomena, it is correct to use
  causal dependent arising as a reason [for establishing its lack of inherent existence]. The second, dependence on parts,
  can be used as well. Also when the subject would have been
  uncompounded space the second kind of reason, depending on parts,
  would be a correct reason as well.


We do not even need to go into the third level of dependent arising (dependence on name) that is posited only by Prasangika to establish that nirvana is empty of svabhāva, is empty of true existence, is empty of existing by way of its own characteristics (all these are synonymous).

We do not need to know either that there is a terminological division of five types of nirvana: non-abiding, abiding, with remainder, without remainder, and natural.


To summarize, nirvana depends on factors that it is not, and without which it would not exist. You can apply this to any phenomena, including permanent phenomena: the person depends on factors (the body, consciousnesses, etc) that the person is not, but without which the person wouldn't be what it is.