When I first read the title of the question, I had a double answer sprung to my mind immediately: yes, it can be done and to great effect, even!
I saw it in two different ways:
a) the main point of the story is not the mystery in itself but the main character
In this situation, the main plot concerns a problem the detective has and which they are trying to solve while, at the same time, trying to discover the criminal.
In an extreme situation, the crime could be left completely unsolved! The subplot could either hinder the MC in solving his true problem, thus having to be set aside, or the attempt at solving it could help the MC find the solution he needs.
b) the main point of the story is discovering the criminal, not necessarily bring him to justice
Well, the heading says it all, I'm afraid. For as long as it's clear that the only thing the story owes the reader is unveiling the criminal, it should still make for a rewarding read.
Then, I read the rest of the question.
My imagination is the detective pointed the wrong killer, jailed ,and after the innocent is hanged, the killer kidnapped the detective where he confront him with his deduction error before he ends him.
A different scenario from my impulsive two, but maybe not so different. It fits nicely with option b): the author must make sure that unveiling the criminal is rewarding enough.
This also makes me think that the main point of the story is not finding the culprit per se, but dealing with the fact that sometimes one's errors have quite grave implications. In this case, it reads as a tragedy: the MC may be led to his downfall by his pride and, in the end, has his eyes opened to both tragic outcomes of his folly: he caused the death of an innocent man... and his own.
Again, there's some affinity with my first secenario: the main point is not so much to discover the criminal but to focus on the MC's character. Balancing his good qualities to almost hide their pride and high self-esteem, even though those two flaws mean he won't be humble enough to have the doubts that might allow him to dig deeper and completely ascertain the identity of the criminal.
I'd actually be quite interested in reading such a tale!