I am searching for a single word that has a definition similar to the phrase 'their own fault'.
I am unaware of a single word bearing this definition, possibly culpable or blameworthy but believe there may be alternatives.
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You could go for self-inflicted:
caused by one's own actions
- a self-inflicted wound
- His problems are mainly self-inflicted.
I suggest onus:
Responsibility for an error or fault; blame: Each side wants to avoid the onus of having started the disagreement.