E.g. First one is:
The incident could have happened.
And the second one is:
The incident could have been happened.
What is the difference in terms of their meaning? Or is there any grammatical mistake?
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There is no difference here. Both are "could have". "Could have" is a modal conditional perfect construction ("would have" being the conditional perfect) when followed by a past participle.
Thus, with the part participle "happened", you get "the incident could have happened".
"Could have been" is just the same, but with the past participle of "to be". Thus, it cannot be followed by any old past participle - your second example is wrong. Not every verb can be used there. Caused, avoided or averted could, in this case. These are constructions where the 'incident' is acting as an object to those verbs, but rendered in the passive voice and thus grammatically looking like a subject for an auxiliary verb. If the verb is intransitive, or cannot meaningfully take the earlier noun as an object, you can't use such a construction. In the first case, that's because intransitives cannot be rendered passive; in the second, it's just because it would make no sense semantically.
It can be followed by an adjective - "the incident could have been serious" - by a progressive participle - "the incident could have been happening" - or by some noun phrases, particularly those that start with an article - "the incident could have been the worst ever".