A drowning man will clutch at a straw

One grabs at the slightest chance when all hope is slipping away. Clutch is comparatively recent and is more suggestive of desperation than the earlier catch. To clutch at a straw (or straws) is frequently used as a metaphorical phrase.

Lyke a man that in peril of drowning catcheth whatsoeuer cometh next to hand‥be it neuer so simple a sticke.
[1534 More Dialogue of Comfort (1553) iii.]

We do not as men redie to be drowned, catch at euery straw.
[1583 J. Prime Fruitful & Brief Discourse i. 30]

The drowning man snatches at every twig. ‥The messengers of Benhadad catch hastily at that stile of grace, and hold it fast.
[1623 J. Hall Contemplations VII. xix. 252]

A drowning man will catch at a straw, the Proverb well says.
[1748 Richardson Clarissa VII. i.]

His gratitude caught at those words, as the drowning man is said to catch at the proverbial straw.
[1877 W. Collins My Lady's Money xv.]

Wang seemed to think my insistence‥very stupid and tactless. But a drowning man clutches at straws.
[1915 Conrad Victory iv. viii.]

A drowning man will clutch at a straw.
[1967 Ridout & Witting English Proverbs Explained 49]

We drift down time, clutching at straws. But what good's a brick to a drowning man?
[1967 T. Stoppard Rosencrantz & Guildenstern are Dead iii. 80]

Related to: hope and despair

Bibliography of major proverb collections and works cited from modern editions is available here.