If the episode about the sick child is any indication, it is possible that one of Do Do-Hee's parent made a deal to save her from some sickness. That car accident was no doubt the 10th year of the contract and was collection day.
However, what I can't remember is if it was hinted before that both of her parents died at the same time. And I don't recall there was a collection day wherein another person died other than the one who made the contract.
If both of her parents died during that car accident, maybe the spouse died first and the one who made the contract still had a chance to live. Unfortunately, for that person, it happens to be collection day.
I think that way it is possible. It was a car accident that Jung Koo Won had nothing to do about. After all, he can just induce a heart failure by visiting them anytime and anywhere; he doesn't need to orchestrate a car accident.
If that parent did not make a contract, s/he would have lived after the car crash, only his/her spouse would've died that night. (Assuming all other variables remained the same.)
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