As for the dog, this is established by textual evidence and scholarly consensus. As for birds, however, the correct view is that whatever they kill is lawful, as we shall mention, Allah willing.
His statement, “What it kills is lawful if it is trained”: the author says, “what it kills,” rather than, “what it wounds,” provided that it is trained—that is, provided that its owner has trained it. Allah, exalted is He, says:
“And those hunting animals which you have trained, training them from what Allah has taught you—so eat of what they catch for you.” [al-Ma’idah 5:4]
How do we know that it is trained? With regard to an animal that hunts with its fangs, it is known to be trained by three signs:
First: it sets off when sent.
Second: it desists when restrained.
Third: when it catches the prey, it does not eat from it.
By our saying, “it sets off when sent,” we mean that, upon seeing game, it does not go off by itself; rather, it goes only when you send it—that is, when you urge it toward the game. The manner of urging it differs from one group to another. It may be done by calling it by the name you have given it and urging it on; it may be done by whistling; or it may be done by any means, according to the conventions of those who train such hunting animals.
By our saying, “it desists when restrained,” we mean that if you say, “Stop!” in the language in which you trained it, it stops.
By our saying, “when it catches the prey, it does not eat from it,” we mean that Allah, exalted is He, says: “So eat of what they catch for you.” For if it eats, it has caught the prey for itself, even if it eats only a small amount. It is therefore not considered trained.