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Yes, they did both commit suicide. I personally think it is because, at that time, the day dream they imagined themselves to be in, where they were not living in such darkness and full of such sorrow, began to fade and they could not bear the thought of returning to their former existences of "perfection" so they decided to kill themselves before that dream had ended.
Also, I think that P had another reason of his own. He knew that, eventually, just killing animals would not be enough for him and he was tormented by his decreasing hold on humanity. Because of this, he did not believe he deserved to love I and chose to end himself before he became even more monstrous than he was.
Hope that helps!
Spoilers...
I so confused.can someone explain Why did they kill themselves? Did they both die at the end?