At my first job, I had the bad luck to get a manager that was, quite literaly toxic.

This was to the point of him driving most of the team to quit. 
In the three month I was there, he drove 5 people to quit (in a team composed of 12 persons), and was growing close to drive the rest of the team to quit.

To give a perspective of why he was toxic : 

 - Constantly undermining every one's work by saying thing like "I could have done it in one hour" or "That was really easy, don't be too proud of yourself"
 - Constantly failing to meet deadlines, wich resulted in everyone else (not him) to stay overtime to try and makes things right (We once had to wait 3 week, for a vital piece of information, and when he delivered it to us, we were one week behind the deadline).
 - Berating the team for using their rights, such as overtime pay.

Now at the time I was lucky enough to have the possibility to leave without too much consequences. But a colleague there was not so lucky, as he needed this job to sustain his family. 

This made me wonder, if there exists any method to, at the very least, mitigate the stress induced by this kind of manager ? When quitting is not an option, and you have to stick with the job ?

As suggested a little more precision on the situation :
 
This happened in france, in a region where the supply of software developper is far higher than the demand, and leaving your job can lead to several months of job hunting.

In France when you quit, it is harder to get monetary compensation than if you were let go.

Also, there was only two people above this manager, there had already been complaints made, but they did not do anything, because he had way too much responsabilities, and the company was basically tied to him, for better or for worse.