לזכות רפואת הרב אורי אהרן בן סעדה
הרב יצחק חיים יחיאל בן אסתר
ולזכות ר' זאב שלמה בן בינה
כל שעה שמותר לאכול, מאכיל לבהמה לחיה ולעופות ..... עבר זמנו, אסור בהנאתו....
[עפ"י דברי הגרח"ש זצ"ל]
The Mishna says [Pesachim 21a]:
AS long as one is permitted to eat chometz, he may feed animals.... and derive benefit, once the time passes, his chometz is forbidden from deriving benefit...
The implication of the Mishna [as the Gemara says], is that after the time one is no longer permitted to eat, he may also no longer feed animals.
Now the Mishna was written very generally and didn't specify specifically his animal. It would appear from this, that once he may no longer benefit from chometz, he is prohibited from feeding even animals that are hefker. However, this is not necessarily the case, because it could be that what the Mishna means is that it is forbidden to feed HIS animal, and the word "animal" relates to HIS animal [because it is only from feeding HIS animal that he benefits].
The source of this issue of feeding the animal of hefker is in the Yerushalmi [הלכה א]
"לא יאכל חמץ [שמות י"ג ג'] היום אפילו לכלבים, הרי זה בא לאוסרו בהנייה. מה אנן קיימין אם לכלבו ההני איסור הנייה, אלא כי נן קיימין אפילו לכלב אחרים. זאת אומרת שאסור להאכילן לבהמת הבקר".
So we see clearly that the conclusion of the Gemara is that it is forbidden to feed an animal that is hefker.
Now the question is if the איסור is included in the איסור הנאה, meaning that even when one feeds hefker animals it is considered that he benefited because his will is being fulfilled when these animals eat. Or perhaps this is not considered הנאה and the איסור is an independent one, that besides the other איסורים of chometz, there is also an איסור not to feed it to an animal, even if the animal doesn't belong to him and he derives no הנאה from this animal's consumption of this chometz. As the Yerushalmi derives from the pasuk "ולא יאכל חמץ" that one may not do something to cause the chometz to be consumed. [See Imrei Binah Pesach 19, Ohr Sameach Maachalos Asuros 4-22]
Since we find that the pasuk from which we derive the איסור is written in the context of Pesach, it could be that this איסור only applies to chometz on Pesach and not to other איסורים. So writes the Makor Chaim [448-10] and he learned this from the Tur and Shulchan Aruch [448-6] who only codify this איסור in the halachos of chometz [and so writes the Gra]. However the Tashbetz [3-293] cites the Yerushalmi and writes that for this reason even other איסורי הנאה may not be fed to animals. According to this approach, we should explore whether this din applies to איסורי הנאה that the Torah created or maybe it applies to ALL איסורי הנאה including what a person forbade to himself with a neder.
The Makor Chaim [448-10] writes that just as one may not feed an animal one may also not feed a Gentile. Based in this he writes that according to Tosfos [22b ד"ה ואבר] it is clear that this איסור doesn't apply to other איסורי הנאה. The Ohr Sameach [פ"ד מהל' מאכלות אסורות הכ"ב] questions this, see there. The Imrei Binah [ibid] explained that the Makor Chaim was referring to the BEGINNING of Tosfos there, who writes that it is permitted to hand a Gentile an אבר מן החי that belongs to him. On this, the Makor Chaim asked that this should be forbidden because he is causing the Gentile to eat and is no better than the איסור of feeding איסורי הנאה to an animal that is hefker??!
The Imrei Binah resolved this question by saying that even if we say that it is forbidden to feed איסורי הנאה to an animal and a Gentile, nevertheless when one hands over to the Gentile איסורי הנאה that belongs to him, he transgresses no איסור. This is because ANYWAY it belongs to the Gentile and it is not considered as causing him to eat.
[עפ"י דברי הגרח"ש זצ"ל]