That varies greatly throughout languages.
In ergative Sumerian (which did not necessary have copula sentences, for there has been no commonly accepted theory of Sumerian syntax and Sumerian had polypersonal-like clauses similar to those of modern Basque) a subject of an equative sentence was in Absolutive case:
za-e lugal ursag-me-en [thou+ABS king+ABS hero+ABS-art] = Thou art the king, the hero.
There are no exactly copula sentences in Sumerian with (presumably) sentence-final existensial verbs.
Ergative was used mostly as a case to express an animate subject (although there were some examples of birds or cities mentioned in the same case as ergative subjects, these words were regarded in Sumerian as inanimate).
The concept of equation was expressed in Sumerian by Equative case and, in some examples, by Comitative (namely, in phrases like comparing oneself with smb).
In Basque, subjects of equative sentences are often presented by Absolutive regardless on their animacy/inanimacy, e.g.:
Hiri hori oso polita da. = [Town that very beautiful is]. = That town is very beautiful
Basque also has sentence-final equative verbs, but sentence-final verbs are not copulas.
Just like Japanese, which has sentence-final [equative] verbs and/or adjective predicates, and Equative -yori, but there is no Ergative in Japanese.
Alternatively, Finnish language has two forms of adjective predicate with preceding (existential) copula, but there is no Ergative in it, either. Well, at least there is no explicit ergativity in its commonly recognised system.
Therefore, of all the languages I am familiar with, Sumerian seems to be the only language matching the criteria you have set.