Synonyms for Droop:

n.

cascade, hang out, sling, string, suspend. flop, lop, slouch, tire, weary, do for, feel/be slow, run out of gas, run out of gas/steam, run out of/lose steam. better. droop (noun)
flag, loll, sag, swag, wilt.
sag (noun)
languish, lean, sink, weaken, hang down.
shape (noun)
sag.

v.

hang (verb)
bob, dangle, drape, hang, loll, nod, sag, sway, swing, trail, Draggle.
hang down; languish (verb)
dangle, flag, lean, loll, lop, sag, sink, sling, slouch, suspend, weaken, wilt.
motion (verb)
flag, sag, swag.

Other synonyms:

languish, lop, weaken. hang out, tire, weary. flop, slouch, suspend. do for. cascade. sling. string. fall asleep
nod.
wilt
wilt.
Other relevant words:
better, cascade, flag, flop, languish, lean, lop, sink, sling, slouch, string, suspend, swag, tire, weaken, weary, wilt, hang down.

Usage examples for droop

  1. She looked at him as he passed her, but did not speak; of course, she guessed his errand, for he saw her head droop a little over the flowers. – Lover or Friend by Rosa Nouchette Carey
  2. And a little bit more shade under the chin, and the wistful droop of the mouth relieved, oh, a very little bit! – Four Girls and a Compact by Annie Hamilton Donnell
  3. He sat during breakfast with bandaged eyes, and a droop of the shoulders, that seemed to say old age had come upon him in a single night. – The Magnetic North by Elizabeth Robins (C. E. Raimond)