E. Cobham Brewer 1810–1897. Dictionary of Phrase and Fable. 1898.
Elbows.
Out at elbows. Shabbily dressed (applied to men only), metaphorically, short of money; hackneyed;
stale; thus, we say of a play which has been acted too often that it is worn out at elbows. It is like a coat which is no longer presentable, being out at the elbows.
