I am a native speaker of AmE. I understand when and where to use their vs theirs, etc. etc. (i.e. Don't migrate this to ELL!). I've searched the site and google, and I have not quite seen an answer to my question.
Etymonline describes the word theirs as:
possessive pronoun, "their own," early 14c., from their + possessive -s, on analogy of his, etc. In form, a double possessive.
plural possessive pronoun, c. 1200, from Old Norse þierra [sic] "of them," genitive of plural personal and demonstrative pronoun þeir "they" (see they). Replaced Old English hiera. As an adjective from late 14c. Use with singular objects, scorned by grammarians, is attested from c. 1300, and OED quotes this in Fielding, Goldsmith, Sydney Smith, and Thackeray. Theirs (c. 1300) is a double possessive. Alternative form theirn (1836) is attested in Midlands and southern dialect in U.K. and the Ozarks region of the U.S. Emphasis mine
(Parenthetical question, what do they mean by use with singular objects in this case?)
The entries for our and ours are similar.
Why does English have a double possessive pronoun? And why does modifying it thusly change its usage? Singular-plural possessive pronoun - possessive adjective; double-plural possessive pronoun - possessive pronoun?
Theirs is used when there is not a following noun, but, I don't understand why a double possessive would be used in this way.
The book is theirs.
That is their book.
We cannot say:
The book is their.
That is theirs book.
But, for the life of me, I cannot figure out why making it a double possessive would make this happen!