As a follow-up to this discussion our Gemara talks about two or more groups whose sacrifices become intermingled to the extent that they do not know which animal belongs to whom. The suggestion of the Gemara is to have one person from each group announce his intention to leave the group and join another. Once each of them has agreed to join the other group, both groups makes the following conditional statement to the new member of the group:
If this Paschal lamb that is now in our possession is ours, you are withdrawn from the Paschal lamb that was yours, and your are registered for our Paschal lamb and you may eat from it. And if this Paschal lamb is yours, meaning that it actually belongs to the other group, including this individual, we are hereby withdrawn from ours and we are registered for your Paschal lamb, which you agree to share with us.
By doing this, the people of both groups succeed in arranging to sacrifice the animal belonging to the group that they had joined.
The Tosafot Ri”d points out that this is not the usual procedure when two sacrifices get mixed up. If two similar korbanot are confused, we usually rule that both should be brought normally and that each one will fulfill the role that it needs to, even if we do not know which korban belongs to which person. The situation is different with a korban Pesah. As noted before, a person must join a group in order to participate in the Passover sacrifice. The korban that will be brought must belong to that group, or else the korban is invalid. It is therefore essential that we ascertain who the animal belongs to. When it is impossible to sort it out we solve the problem by recommending that the exchange described above takes place in order to ensure that the sacrifice is eaten by the group to which it truly belongs.