expression, adverb
hoping against hope; desperately hoping; as a last hope
An idiomatic expression describing a situation where one clings to even the slightest, most unreliable hope, like a drowning person grasping at a straw. Often used adverbially to modify verbs of seeking, asking, or relying.
藁にもすがる思いで、彼はその情報を信じた。
Hoping against hope, he believed that information.
藁にもすがる思いで、私はその治療法を試した。
As a last hope, I tried that treatment.
A similar proverb meaning 'to grasp at straws'; 藁にもすがる思いで is the adverbial form expressing the feeling of doing something out of desperation.
From the image of a drowning person grasping at even a floating straw (藁). The phrase 藁にもすがる (to cling even to straw) is combined with 思い (feeling) and the particle で to form an adverbial expression.