This question mayh be divided into three parts:

(a) How could Abaye punish the parents of Rav Papa in such a cruel manner with no apparent guilt on their part?

(b) How could Abaye "place his eyes" on Rav Papa's parents when they were not present? An "Ayin Ha'ra" is only effective when a person actually sees the subject that it affects (see, for example, Berachos 20a).

(c) Why did the "placing of the eyes" effect Rav Papa and his parents, such that his parents died, if neither he nor they had done anything wrong and they did not deserve to die?

The answers to these questions seem to be as follows:

(a) Every "placing of the eyes" that we find in Shas (let us call it, for the sake of simplicity, "Ayin Ha'ra") involves a feeling of the jealousy (Kin'ah) of a Chacham (or person) towards the deeds of his colleague, even if that feeling is very slight. Certainly, he has no intention to cause his colleague to be punished, as the YA'AVETZ here writes at length. Nevertheless, since the Chacham was distressed as a result of his colleague's deeds, his pain effects a process of retribution towards the one who pained him. This is the case with every "Ayin Ha'ra" mentioned in Shas. When it involves a Chacham, even the most minute distress of jealousy can cause someone to be punished as a result. (Note from Rav Yosef Pearlman: See Avos 2:10, "Hevei Zahir b'Gachaltan..., and the commentaries there.)

(b) The "Ayin Ha'ra" was not placed upon the parents of Rav Papa, but rather upon Rav Papa himself, who had achieved great success in his learning due to the efforts of his parents in supporting him and his family (as Rashi explains). Now that his parents had died, it would be very difficult for him to continue learning with the degree of Hasmadah with which he had learned until now, since he would now have the burden of supporting his family himself.

(When the Gemara says that Abaye "placed on them his eyes," it is not to be taken literally. It means that by placing his eyes on Rav Papa , his parents died. Alternatively, the Gemara should indeed say "he placed on him his eyes," as it appears in the Munich Manuscript of the Talmud.)

(c) The parents of Rav Papa certainly did nothing against Abaye. It seems that their destined time to depart this world had already arrived (and passed), and the only reason they were given extra time in this world was in the merit of supporting their son, the Tzadik, Rav Papa. Now that Rav Papa was no longer deserving of their support, his merit was removed from them and they died.

It is more difficult to understand, though, what misdeed Rav Papa committed here. After all, a person is certainly obligated to point out to his Rebbi an error in a Halachic ruling! How can Rav Papa be held accountable for this?

It must be that Rav Papa was expected to correct Abaye's error in a more respectful manner, even more respectful than saying, "But does not the master hold that...." Rather, he should have said, "Is it not written in the Torah such and such," or, "Did we not learn such and such..." (as mentioned in the Shulchan Aruch, YD 240, based on the Gemara in Kidushin 32a). Perhaps he was held accountable for not immediately saying both of the rulings ("on condition that he give 200 Zuz," and "Meshateh Ani Bach"), but rather he waited until Abaye made a mistake in the second Halachah until he corrected him, and that was certainly inappropriate (as the Gemara says in Shavuos 31a).

Ha'Rav Moshe Shapiro, shlit'a, explained to me that Rav Papa did not sin at all. Rather, the death of his parents was for his benefit, so that he would be able to learn Torah through adversity and thereby acquire an eternal share in Torah.

M. Kornfeld