Vedantic thought overlays the five koshas with a coarser scheme of three bodies, or sharira: the gross, sthula sharira, the subtle, sukshma sharira, and the causal, karana sharira. Anandamaya, the bliss sheath, is identified with the causal body alone, the subtlest of the three and the last to dissolve, distinct from Annamaya, the food sheath, which is the gross body and the first to be shed at death.
Because Anandamaya constitutes the entire causal body by itself, Vedantic teaching treats it as the final covering the true self must be recognised as distinct from before liberation is complete; ordinary deep, dreamless sleep is described as a temporary and unconscious brush with this sheath, a state of bliss without awareness of it, which liberation is said to make permanent and fully conscious.
This is also why Anandamaya, despite being called a sheath, is described in the tradition as the covering nearest to the self of any of the five, closer than a covering ought to be, a paradox the texts resolve by treating full liberation as the shedding of even this last, subtlest layer. Twentieth century Theosophical writers later borrowed kosha terminology for a separately bounded scheme of subtle bodies, a distinct later system built on borrowed vocabulary rather than a restatement of this Vedantic teaching.
Sources The Principal Upanishads with Rainbow Body: A History of the Western Chakra System from Blavatsky to BrennanKurt Leland