Pe'ah, Chapter 2, Mishnah 8. The Mishnah continues the principle explained in the previous Mishnah - that the obligation of pe'ah depends on the reaping being done by the owners themselves, as in "u'ketzartem" ("and you shall reap"). From this, three cases follow: a field part of which was reaped by others, a field half of which was sold, and a field that was consecrated and then redeemed.
"Ketzaruha listim chetzyah":
Robbers entered the field and reaped half of it, "ve'katzar hu chetzyah" - and the owner reaped the second half himself - "nosein pe'ah mimah shekatzar" - he gives pe'ah from what he reaped. That is, he is obligated in pe'ah, but only from the portion he reaped himself and not from the portion the robbers reaped, since that reaping is not included in "u'ketzartem".
"Katzar chetzyah umachar chetzyah":
The owner reaped the first half and sold the second half to another person - "haloke'ach nosein pe'ah lakol" - the buyer gives pe'ah for the entire field from the half he purchased. This makes sense, since both halves were reaped by their owners - the first by the first owner and the second by the second owner - and in both cases "u'ketzartem" is fulfilled.
And the reason the second one is obligated in pe'ah for everything is this: the obligation of pe'ah rests upon the standing grain, so that the pe'ah will be taken from the grain that remains standing at the end. It emerges that when the seller sells the second half, it is as though he said to the buyer: be aware that what I am selling you is less the amount that must be set aside as pe'ah for this entire field.
"Katzar chetzyah ve'hikdish chetzyah":
He reaped the first half and consecrated the second half, so that it belongs to hekdesh (the Temple treasury). Hekdesh itself is not obligated in pe'ah, but if a person came and redeemed it from the hand of the treasurer - "hapodeh miyad hagizbar, hu nosein pe'ah lakol" - the one who redeems it from hekdesh reaps that half, and his law is like that of the buyer: he gives pe'ah for the entire field, even for the first half. For at the moment he consecrated the second half, the pe'ah obligation of the entire field was resting upon that half. As long as it was in the possession of hekdesh no obligation applied to it, but once the second person redeemed it and reaped it, he is obligated to separate pe'ah from it for the entire field.
In summary: In this Mishnah we learned three cases that emerge from the principle that "u'ketzartem" requires reaping by the owners: robbers reaped it - he gives pe'ah only from what he reaped himself; he sold half of it - the buyer gives pe'ah for everything, since the pe'ah obligation rests upon the standing grain and it was sold to him on that basis; he consecrated half of it - the one who redeems it from the hand of the treasurer gives pe'ah for everything, since once that half left the possession of hekdesh, the pe'ah obligation of the entire field returns and takes effect upon it.