Nirvana has inherent existence but is empty. although nirvana inherently exists, it is not a 'self'. it is not-self (anatta). it is empty of self (sunnata). the logic of Nagarjuna sounds questionable, in appearing to assert a synonomity between 'existence' and 'self'.
if "not-self" did not inherently exist, then how could all things be not-self? this simple statement refutes the logic of Nagarjuna
Whether or not there is the arising of Tathagatas, this property stands — this regularity of the Dhamma, this orderliness of the Dhamma, this this/that conditionality (iddapaccayatta). Paccaya Sutta Monks, whether or not there is the arising of Tathagatas, this property stands — this steadfastness of the Dhamma, this orderliness of the Dhamma: All processes are inconstant. Whether or not there is the arising of Tathagatas, this property stands — this steadfastness of the Dhamma, this orderliness of the Dhamma: All processes are unsatisfactory. Whether or not there is the arising of Tathagatas, this property stands — this steadfastness of the Dhamma, this orderliness of the Dhamma: All phenomena are not-self. The Discourse on the Orderliness of the Dhamma