The gemara (Sukkah 27b) darshens the pasuk “kol ha’ezrach b’Yisrael yeishvu ba’sukkos” to mean that a single sukkah owned by one person may be used by even all the Jewish people so long as they take turns. The gemara concludes from here that there is no requirement to own one’s own sukkah. Rashi is troubled by the logic of this derasha. Maybe ownership of a sukkah is required; the pasuk allows even the entire nation to use a single sukkah because it is speaking of a sukkah jointly owned by everyone. Rashi answers that such a case is impossible. If the entire nation owned a single sukkah, the worth of each person’s share would be less than a perutah. Such a minute stake does not count as a partnership. (See Minchas Chinuch 325 for more on this Rashi.)
Yet, the gemara (Kiddushin 41) accepts the possibility of a korban Pesach jointly owned by all of klal yisrael. The gemara rejects “v’shachatu oso kol kahal adas yisrael” as a source for shlichus, even though one person does shechita on behalf of the entire community, because that may be a unique case where everyone whom the shliach is acting for has a share in the korban. Why in this case do we not apply Rashi’s rule? If all of klal yisrael were to share in one korban, the stake of each person would certainly amount to less than a perutah; it should be so negligible as to be meaningless?
Let me take one possible answer to this problem off the table right away. You could reject the premise of the question and argue that the korban pesach necessitates minuy – being counted as a participant – but minuy does not require ownership. My son’s birthday was last week and his present was an Imrei Binah, which raises this issue (Hil Pesach end of siman 2). The I.B. opines that a kinyan is required for minuy. Granted you could debate his proof and argue otherwise, but for now let's avoid that debate. How else might you answer this question?