All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
What is meant by designating a sacrificial animal is that a person explicitly declares of a specific animal from his livestock: "This is my sacrificial animal," or "I have made this my sacrificial animal," or "I am obligated to sacrifice this one." Once such a declaration is made, the animal passes out of his ownership — he is no longer permitted to dispose of it freely, it remains in his custody as a trust, and it takes on the ruling of a vowed designated sacrifice. Imam al-Shirbīnī, may Allah have mercy upon him, stated: "Whoever vows a specific sacrificial animal — saying, for example: 'It is upon me for the sake of Allah to sacrifice this cow,' or 'I have made it a sacrificial animal,' or 'this is a sacrificial animal,' or 'I am obligated to sacrifice it' — even without explicitly saying 'for the sake of Allah' — his ownership over it ceases and he is obligated to slaughter it at the designated time." — [Mughnī al-Muḥtāj, Vol.6/P.130]
An exception is noted among some Shāfi'ī scholars: if a person says "This is a sacrificial animal" or "I have made it a sacrificial animal" intending merely to inform rather than to commit, it does not become obligatory. Shaykh Bā'ashn, may Allah have mercy upon him, stated: "What commonly occurs among ordinary people when they say 'this is a sacrificial animal' — often without knowing the implications — or even if they intend merely to inform... it becomes a vow according to Ibn Ḥajar and al-Ramlī. However, al-Sayyid 'Umar al-Baṣrī said: this is applicable only where there is no intention of mere informing; if such intention exists, the designation does not take effect." — [Bushrā al-Karīm, p. 694]
Verbal utterance is a condition for valid designation. If a person merely intends in his heart to make an animal a sacrificial offering without actually saying so, it does not become a designated sacrifice. Imam al-Shirbīnī stated: "Note: his use of the phrase 'he said' indicates that if a person merely intends in his heart to make a sheep or camel a sacrificial animal without uttering it, it does not become one — and this is the sounder position." — [Mughnī al-Muḥtāj, Vol.6/P.130]
If the designated animal is damaged, defective, or lost:
• If this occurs before the time of the uḍḥiyyah enters and before the person was able to slaughter it, and without any negligence on his part — he bears no liability whatsoever.
• If this occurs after the time has entered and he was capable of slaughtering it but delayed — he becomes financially liable due to his negligence in delaying the slaughter.
Imam al-Shirbīnī stated: "If it perishes — meaning the vowed designated sacrifice — before the time, or during the time but before he was able to slaughter it, without negligence on his part, then there is nothing upon him due to his lack of negligence, and it is in his hands as a trust... If the time enters and he was capable of slaughtering it and it perishes, he is liable due to his negligence." — [Mughnī al-Muḥtāj, Vol.6/P.131]
• If the animal is damaged or destroyed by a third party, that person is liable for its value, and the owner is obligated to purchase a comparable animal and sacrifice it. Imam al-Shirbīnī stated: "If a third party destroys it, he is liable for its value as with all valued property. The one who made the vow takes the compensation and purchases a comparable animal with it. If a comparable animal cannot be found, he purchases the closest available. If the destroyed animal was, for example, a two-year-old sheep and the compensation falls short of its price, he takes a one-year-old sheep from it, then a two-year-old goat, then something of lesser value from the sacrificial category, then a share in a sacrificial animal, then meat — and the apparent purport of their words is that the meat need not be of the same type as the vowed animal. He then gives the remaining money in charity out of necessity." — [Mughnī al-Muḥtāj, Vol.6/P.131]
• If the owner himself destroys or neglects the animal, he is obligated to purchase with its value a comparable animal of the same species, type, and age, and sacrifice it during the time of the uḍḥiyyah due to his transgression. Imam al-Shirbīnī stated: "If the one who made the vow destroys it or was negligent, he is obligated to purchase with its value a comparable animal in species, type, and age, and to slaughter it during the mentioned time of sacrifice — due to his transgression." — [Mughnī al-Muḥtāj, Vol.6/P.131]
In conclusion, whoever declares of an animal he owns: "This is my sacrificial animal," or "I have made it my sacrificial animal," or "I am obligated to sacrifice it" — without intending mere information — has designated it as a sacrificial animal, and it takes on the ruling of a vowed sacrifice. He is no longer free to dispose of it, and it becomes obligatory upon him to sacrifice it.
However, if his intent was merely to inform, it does not become obligatory according to some Shāfi'ī scholars — and this position is more accommodating for ordinary people, who generally cannot distinguish between such fine nuances of meaning.
If the designated animal perishes before the time of slaughter and before the ability to slaughter it arises, the one who designated it bears no liability. If it perishes after the time has entered and he was capable of slaughtering it, he is liable and must slaughter a comparable animal in its place — due to his negligence. And Allah Almighty knows best.