Upon whom does the sin fall—the husband or the wife—if the wife is utterly fed up with her husband's ill-treatment of her, especially in bed, which has led her to consider pursuing a path of vice to compensate for the deficiency after his death? And what is the Shar'i ruling in this case?

What you are talking about is very dangerous, and a believing woman should not even think about it, let alone practice it.

The husband's shortcomings do not justify falling into the forbidden. It was possible to confront him or ask for a divorce.

The burden of sin falls on its perpetrator: "For it is what it has earned, and against it is what it has earned" and "Every soul, for what it has earned, will be detained."

What is incumbent upon you is sincere repentance, regret for what has passed, and a firm resolve not to return to it, and to increase in righteous deeds: "And indeed, I am Forgiving to him who repents, believes, and does righteousness, and then is guided."