The halter that elevates and holds in place human mammary glands, named for the inventor Phillipelde Brassiere.
Sometime in the mid twentieth century somebody started calling them bras, maybe because they could spell brassiere. Hardly any store advertises or customers ask for brassieres today. It's simply bra.
Broke, penniless, without means, on the bones of yer arse.
Comes from the cockney rhyming slang 'boracic lint' (a type of medical dressing): Boracic lint = skint.
Boracic is pronounced 'brassic'.