Are there native expressions in oral and formal writing English about something happened - mostly negative incidents or events, but those, who should be responsible for it , don't want to undertake its responsibility or involve themselves in this.
A common phrase in the US is pass the buck
(informal) to evade blame or responsibility by trying to pass it to someone else
A countervailing phrase came into later usage, the buck stops here, to signify that the speaker was accepting responsibility.
Often the concept is expressed by negating terms for taking responsibility, as in
No one would step up
Not a single one of them would take the bull by the horns.
Won't anybody man up? [A bit sexist.]
Depending on the situation, mainly how people react to the problem, there are three different categories of expressions that may fit what you are looking for:
They blame someone else for the problem - They can be accused of "finger-pointing" or finding an "escape-goat".
They actively try to hide the problem - They can be said to be "sweeping things under the rug".
They try to pretend the problem doesn't exist - This is known as an "elephant in the room" that no one wants to talk about.
Otherwise, if they simply refuse to do anything about a problem, I would use the phrase "avoiding their responsibilities" or even "shirking responsibilities".