Student or Learner
If somebody says about someone else that he can't buy a break, does it probably mean that that person can't take a break?
Some guys were looking for their friend who shot someone in the past and now was on the run. They found out he ended up in a town full of bad people, drug dealers, killers.
One of his friends said: He can't buy a break, can he? The one town he picks turns out to be teeming with killers.
So it doesn't mean that he for example cannot get some break from killing, from bad people.
The guy wanted to escape from the old world which was very violent, he killed people, some other people tried to kill him and he wanted to find a quiet, peaceful place.
So when his friends found out that he accidentally ended up in a violent place the same he left behind, one of them asked: Can't he buy a break?
I take it to mean: Can't he have a break (from bad people, killing, violence etc.)
A break, as used here, and as Gil explained, means that something goes easily for someone.
We caught a break. -- Something good happened that helped us.
Can't a guy get a break? -- Nothing seems to go right for me!
He can't even buy a break. -- Even if good luck were available for purchase, it doesn't apply to him. Nothing goes right for him.
It has NOTHING TO DO with the idea of "taking a break" (a rest, a temporary cessation) from something.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.