In the gemara we see various claims that a buyer from a borrower can claim against the ba'al chov. I think it is worthwhile summarizing and explaining when each is applicable.
1. הנחתי לך מקום לגבות הימנו - The buyer can make this claim if he left behind some property in the hand of the borrower, to force the lender to collect from the borrower (even if it is ziburis). This does not apply when the second buyer claims to have left behind by the first buyer (Tosafos), since the entire claim is based on the premise that you cannot collect from משעובדים when there is בני חורין.
2. אי שתקת ושקליתו כדינייכו שקליתו ואי לא מהדרנא וכו - This claim is really a threat that allows the buyer to give beinunis to a nizuk by threatening to otherwise return the ziburis to the seller (who is the mazik) and force the nizuk to collect beinunis. This does not work to force a ba'al chov to collect ziburis because he can call the bluff and say "go return it". In other words, the threat only works when if carried out, would force the one who is collecting to take a lower grade than you are trying to make him collect now. Also, the concept of returning only is binding from this point forward, as if the seller would be purchasing a new property now. Therefore, it doesn't work by Yesomim who are not obligated to pay their father's debts from their own purchases (Tosafos). Rosh disagrees and holds that this threat can even force a ba'al chov to get beinunis because every threat that can be done, it is as if it were done and the other can never call his bluff.
3. אנא בהא תקנתא לא ניחא לי - A buyer who purchased ziburis, then beinunis, then idyis, one after the other, has the ability to force all people that are making claims on the sellers property to collect from ziburis, by forfeiting the takana d'rabonon of not collecting from m'shubadim when their are b'nei chorin.
4. מה מכר ראשון לשני כל זכות שתבא לידו - This claim empowers a second buyer to make any claim that the first buyer would have made. Therefore, if buyer #1 who purchased all the fields from the seller, went and sold idyis to buyer #2, then buyer #2 can force everyone to collect from the beinunis and ziburis left behind by buyer #1, since if buyer #1 would have retained the idyis, he would not have given it up (rather he would claim he doesn't want the takana d'rabonon).
5. להכי דייקי וזבני עידית וזיבורית ארעא דלא חזי לך - This claim applies to a case where buyer #1 sold to buyer #2 idyis and ziburis, and now has a b'al chov claiming the from #2. Buyer #2 cannot claim that he left behind beinunis for him to collect from (הנחתי לך מקום לגבות הימנו), because the ba'al chov can claim that he prefers to collect ziburis [Tosafos d.h. aval, and Rashi 7b d.h. v'iy, hold that a ba'al chov can choose from either beinunis or ziburis, and a nizuk can choose from idyis, beinunis and ziburis. The Rosh holds that the b'al chov only has a claim on beinunis, not on ziburis]. Nevertheless, buyer #2 can claim that he specifically bought types of fields that the ba'al chov either has no right to (idyis) or is not likely to collect from (ziburis), and force the ba'al chov to collect beinunis from buyer #1.