Śeṣatva — The Soul's Essential Nature as Wholly Belonging to Bhagavān
Śeṣatva (Sanskrit: śeṣa = remainder, one who is subservient, one who belongs to another; -tva = the abstract suffix denoting essential nature or '-ness'; cf. Tamil form śeṣatvam) denotes the fundamental ontological quality by which every ātmā is, in its truest nature, entirely the property (sva) of Bhagavān Śrīman Nārāyaṇa. This is not merely an ethical or devotional claim but a metaphysical statement about the soul's constitution: it is a śeṣa (one who belongs) in relation to the śeṣī (the owner, Bhagavān). The soul does not belong to itself, nor to any worldly relation, nor to any intermediary deity; it belongs, at its very root, to Bhagavān alone — a truth that saṃsāra continuously obscures and that liberation fully reveals and enacts.
Grammatical and Philosophical Basis: Piḷḷai Lōkācāryar in Mumukshuppadi invokes the Sanskrit grammatical rule by which the genitive case (ṣaṣṭhī vibhakti) signifies a śeṣa-śeṣī relationship — the owned and the owner. Just as 'Devadatta's cow' (devadattasya gāuḥ) establishes that the cow belongs to Devadatta, the scriptural expression 'Bhagavān's ātmā' (nārāyaṇasya jīvaḥ) establishes the soul's śeṣatva in relation to Īśvara. Āchāryas explain this is not a secondary or derived relationship imposed from outside — it is the primary svarūpa (essential nature) of the ātmā, eternally so, whether the soul is in bondage (saṃsāra) or in liberation (Paramapadham). The difference between a bound soul and a liberated soul is not that one has śeṣatva and the other does not; it is that the liberated soul knows and lives its śeṣatva consciously while the bound soul is ignorant of it.
Ananya-śeṣatva: The full import of śeṣatva in Śrī Vaiṣṇava soteriology is ananya-śeṣatva — the soul's belonging to Bhagavān exclusively, not even to itself. This rules out any self-reliant or self-directed spiritual effort as the ultimate upāya (means): since the soul does not own itself, it cannot 'offer' itself to Bhagavān as a self-generated gift. What prapatti accomplishes is not the creation of a new relationship (śeṣatva already exists) but the soul's recognition and acceptance of the relationship that has always been true. This is why ākiñcanya (utter helplessness, having nothing to offer) is the first qualification of a prapanna: it is simply the honest acknowledgement of what was always the case.
Relation to Bharatva and Pāratantrya: Śrī Vaiṣṇava theological analysis describes the soul's relationship to Bhagavān through three complementary terms that together constitute the full picture of jīva-Īśvara sambandha: śeṣatva (the soul belongs entirely to Bhagavān — Bhagavān is the śeṣī), bharatva (the soul is borne, sustained, and protected by Bhagavān — Bhagavān is the bhartā), and pāratantrya (the soul is entirely dependent on Bhagavān for its being and action — Bhagavān is the soul's very ground). These three are not separate doctrines but different facets of the one inseparable reality of Viśiṣṭādvaita: the soul as Bhagavān's śarīra (body), Bhagavān as the soul's śarīrin (inner Self and sustainer). The term śeṣatvam — the Tamil-influenced nominative form — is the same concept expressed in the grammatical form more natural to Tamil Śrī Vaiṣṇava usage, and is treated as fully interchangeable with śeṣatva.