The expression “to lose one’s shirt” means to lose everything one has, and, though this expression is fairly new, the concept of one’s shirt being the last thing one possesses, next to his skin, is not exactly new.
Chaucer conveyed that thought when, in “The Wyf of Bathes Tale,” he wrote, “Who that holt (hold) him payd of his povert (poverty), I holde him riche, al (though) had he nought (not) a schert.”
It is the same idea which, for several centuries also, others have had in speaking of one who has “not a shirt to his back,” or who had “given away the shirt off his back”, the last of his possessions, that is.