I wouldn't want it happened to me.
No, it's not correct. You can say: I wouldn't want it to happen to me. (now or in the future) I wouldn't want it happening to me.
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No, it's not correct. You can say:
I wouldn't want it to happen to me. (now or in the future)
I wouldn't want it happening to me. (now or in the future)
I wouldn't want it to have happened to me. (in the past)
While it refers to a hypothetical or imagined situation, it is not an explicit conditional sentence.