Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Brother, we really appreciate your question, which shows how interested you are in becoming well acquainted with Islam and its teachings. May Allah bless your efforts in the pursuit of knowledge!
Muslims slaughter animals during `Eid in emulation of Prophet Abraham who was about to slaughter his son, Isma`eel (Ishmael), to show obedience to Almighty Allah, when Ishmael was redeemed by a ram brought to Abraham by Angel Gabriel. The Angel then conveyed to him Allah's Command to slaughter the ram instead.
With regard to your question, the late Sheikh Ibn `Uthaymeen, a prominent Saudi Muslim scholar (may Allah shower mercy on his soul), said:
If the sacrificial animal gets injured (develops a flaw), it may still be slaughtered, and this will suffice. An example of that is when a man buys a sheep to sacrifice it, then its leg is broken and it is unable to walk and keep up with the rest of the flock, after he has selected it for sacrifice. In this case it may be slaughtered, and this will suffice because when it was selected, it became a trust, like something that was entrusted to him. Because it is something entrusted and the injury was not the result of his action or his negligence, he is not obliged to offer any guarantee.
Excerpted with modifications from: www.islam-qa.com
Read also:
The Concept of Animal Sacrifice in Islam
Offering Sacrifice on `Eid Al-Adha: Obligatory?
Defective Sacrificial Animal: Can It Be Accepted?
Is Islamic Slaughtering Cruel to Animals?
If you are still in need of more information, don't hesitate to contact us. Do keep in touch. May Allah guide us all to the straight path!
Allah Almighty knows best.