Lord Shiva is unborn and eternal. There is no birth and no death for Him. Lord Shiva is Brahman.
This is what Mahabharatha says about Lord Shiva
Mahadeva is Eternal Brahman. Persons endued with Yoga; Yoga's achievements are unable to know in even a hundred years, the glory and puissance of the great Deity in their entirety. Verily, the beginning, middle or end of Mahadeva cannot be apprehended by the very deities. Indeed, when the case is such, who is there O Madhava, that can recite the attributes of Mahadeva in their entirety?
The Supreme Spirit hath three conditions. In the form of Brahma, he is the Creator, and in the form of Vishnu he is the Preserver, and in his form as Rudra, he is the Destroyer of the Universe!
This is what Sri Swami Sivananda says about Lord Shiva
Siva means that which is eternally happy or auspicious, Parama-Mangala. Om and Siva are one. Mandukya Upanishad says: Santam Sivam Advaitam. Even an outcaste can meditate on the Name of Lord Siva.
Lord Siva is the Supreme Reality. He is eternal, formless, independent, omnipresent, one without a second, beginningless, causeless, taintless, self-existent, ever free, ever pure. He is not limited by time. He is infinite bliss and infinite intelligence.
This is what Sri Adi Shankaracharya says about The Brahman or the Supreme Spirit, synonymous with Shiva
Neither can I be termed as energy (prana), nor five types of breath (vayus), nor the seven material essences, nor the five coverings (pancha-kosha). Neither am I the five instruments of elimination, procreation, motion, grasping, or speaking. I am indeed, That eternal knowing and bliss, Shiva, love and pure consciousness.
This is what Sri Ramakrishna Paramhansa says about Brahman:
The truth established in the Vedas, the Puranas and the Tantras is but one Satchdananda. In the Vedas it is called Brahman, in the Puranas it is called Rama, and in the Tantras it is called Shiva. One Satchidananda is called Brahman, Rama and Shiva.
The formless God is real , and equally real is God with form. It is like an infinite ocean, water everywhere, to the right, left, above, below. Water enveloped in water. It is the water of the great cause, motionless. Waves spring up when it becomes active. Its activities are creation(Brahma), preservation(Vishnu) and dissolution(Shiva).
So in conclusion, Lord Vishnu, Lord Shiva are eternal and never born, they never die. They are the two modes of the Supreme Spirit Brahman. Thus Being Ishvara, they are eternal and supreme. This is Advaita. All the best.