[grasp|clutch] at straws

to be willing to do whatever necessary to improve one's current situation, regardless of one's chance of success

The idiom "grasp at straws" originates from the practice of a drowning person desperately trying to save themselves by reaching for any floating straws or objects within their reach. Figuratively, it is now used to describe a situation where someone is in a state of extreme desperation, willing to consider even the most unlikely or feeble solutions to their problems.

I would have even grasped at the straw of anti-depressants.
Despite the company's financial troubles, the CEO was grasping at straws, hoping for a miraculous turnaround.
When faced with a failing business, he began to clutch at straws, exploring unconventional strategies in the hope of saving it.
She was desperate to repair her damaged reputation and was grasping at straws by seeking public sympathy.
In the midst of a complex legal case, the defendant's lawyer was clutching at straws, presenting weak arguments to the jury.