Lord Rudra is Human destructive aspect of Supreme Shiva or Sada Shiva.
According to Vaishnav philosophy Lord Vishnu as Maha Vishnu lays in the Causal ocean and breathes out the number of universes. How Vishnu creates and maintains the universes is described in my answer here. So when a universe is created, there are 3 personalities that are directly incharge of
- Maintenance-Lord Vishnu
- Creation-Lord Brahma
- Annihilation -Lord Rudra.
Lord Vishnu is Vishnu-Tatva or Sva-amsha(direct expansion) of Maha-Vishnu;i.e. to say Jiva can never become Vishnu in a universe. Brahma is generally a jiva-tatva(Jivatma; a living entity like us) but sometimes when there is no living entity qualified to take up the position of Brahma, Lord Vishnu takes up the position of Brahma.
If in some kalpa there is no suitable living entity who can act in Brahmā’s capacity, Garbhodaka-śāyī Viṣṇu Himself becomes Brahmā and acts accordingly.
Now as I've said in very 1st statement of this question,Lord Rudra is Human destructive aspect of Supreme Shiva or Sada Shiva. That is, He is Shivatma(Shiv-tatva**).
But here is what Srila Rupa Goswami says in His Laghu-Bhagavatamrit.
The scriptures explain that, as Brahma' is, so Siva is sometimes a jiva soul and sometimes an amsa-avatara like Lord Sesha.
Here Rupa Goswami gives analogy of Lord Shesha, thats because Gaudiya Vaishnavas believe that Shesha-Nag on whom Lord Vishnu lies is expansion of Vishnu(Vishnu-Tatva); whereas Shesha-Nag who carries universe on His hoods is a separate ; and He could be a Jivatma sometimes.
Now my question is
Is lord Rudra always an expansion of Shiva(i.e. Sada-Shiva ; just like Anant-Shesha being always an expansion of Lord Vishnu); or can a Jiva become Lord Rudra sometimes in a universe?
** Shiva-Tatva ,Jiva-tatva, Shakti-tatva, Vishnu-Tatva: These are different types of living entities that I've heard of in Vaishnav terminology.