(adj.) devoid of any energy to get things done
Thanks to its commonness, the girls’ name Molly—itself a pet form of Mary—is found hidden away in the bones of a host of English words.
The most familiar of these is probably the verb mollycoddle, meaning ‘to pamper’ or ‘overprotect’: etymologically, Molly appears here as a nickname for a weak or effeminate man, while coddle has been used to mean ‘to treat as an invalid’ since the early nineteenth century at least.
At the less familiar end of the Molly scale are such words as molly-mop (‘a man who busies himself in women’s affairs’), mollymawks (‘an untidy, slatternly woman’), mollyrag (‘to scold or henpeck’), and, albeit with a slight change of spelling, the Scots dialect word mallifuff.
As a noun, a mallifuff is someone utterly devoid of energy; as an adjective, mallifuff would describe someone or something frail or paltry-looking, or else so weak or flimsy as to be utterly incapable of action.
Given that it too derives from the name Molly, we can presume that mallifuff was probably originally a nickname, applied to anyone in a similarly weakened or exhausted state. A fuff, meanwhile, is a soft wisp or tuft of material—so light and insubstantial as to be easily moved by the slightest of breezes. Join those two roots together, and you have a word suitable for those most exhausted, or exhausting, of days.