Abhava is the negative of 'bhava' which means being, becoming, existing, appearance. The word bhava is derived from the Sanskrit root 'bhû' which means to be, to come into being, to become. Therefore abhava means non-existence, the state of non-being.
Existence is the positive state of something and non-existence is the negative state of the same thing, which indicates that something, probably everything, has both positive and negative states of being. Wherever the positive and the negative are discovered to be present in opposition it can be reasonably concluded that the three gunas have separated and manifested, no longer being in a state of equilibrium. Because bhava and abhava are opposites this very duality is indicative that the gunas are involved, rajas being the positive guna and tamas being the negative guna.
The god Brahma, who a personification of the positive guna, at the end of the kalpa is absorbed into Siva Loka, where Siva, the personification of the negative guna, intensely compresses the head of Brahma, constraining it down into transcendental nothingness. Brahma effectively is unable to remember himself and stays in that state of non-existence for aeons of time, compressed into apparent nothingness, his head completely covered by Siva's swaddling body, and disappearing in a state of total self forgetfulness. After an inexorable passage of time, when Brahma eventually stirs, he struggles magnificently to remember himself, but it is not possible to remember yourself unless you love. Brahma remembers himself by discovering the principle of love-existence, which is the principle that existence is possible if all-support-all, and he rises upwards as a bubble, ascending and expanding. Ascending to a region beyond the control of Siva, Brahma escapes from Siva Loka and creation begins again, creation being the positive form of existence. Creation, the golden world of Brahma Loka, is held up by nothing except love, reciprocal love, and hovers above Dissolution, the nihilistic world of Siva Loka, . If that love ever ceases, if someone breaks the bond of reciprocal support, everything, the whole of existence, would fall into the non-existence of Siva Loka again, which always lies below, menacing and threatening. That is the essential nature of the relationship between the two gunas who are eternally in opposition to each other: what one creates the other seeks to destroy. Purusha, the highest witness, sees all this as Prakriti, merely the action and interaction of the gunas, with which Purusha remains unentangled. The Self, oneself as the Absolute, is said to be aloof. Nisargadatta states we are in the universe as the witness (Purusha) and outside of the universe as the Absolute (Parabrahman). Therefore the Absolute is neither existent nor non-existent. Existence and non-existence are states produced by the gunas, and since the three gunas are merely aspects of the mathematical law by which the energy of Shakti manifests as the universe, it can be concluded that both existence and non-existence are part of the illusion produced by Shakti-Maya.
Advaita, particularly Krishna in the Bhagavad Gita, states that that which exists can never cease to exist, and that which is non-existent can never come into existence. Therefore everything that has being must always exist, although it may temporarily be located in a state of non-existence. Everything may oscillate between a state of existence and non-existence, and although completely disappearing it, everything, still exists, although undetectable, in the state of non-existence, which is its negative phase.
Nisargadatta has some interesting things to say about existence and non-existence:
"Existence and non-existence relate to something in space and time, here and now, there and then, which are in the mind. To exist means to be something, a thing, a thought, a feeling, an idea. All existence is particular. Only being is universal. Existences clash, being never clashes. Existence means becoming, change, birth and death, and birth again, while in being there is silent peace. All existence is in space and time and is limited and temporary. He who experiences existence is also limited and temporary. I am not concerned either with what exists or with who exists. I take my stand beyond, where I am both and neither. Do not identify mere existence with reality. Existence is momentary, while reality is changeless and all pervading. Existence is in consciousness, whereas your essence is independent of consciousness. Deny existence to everything except yourself."