Question Summary:
Can one qurbani animal or share be slaughtered on behalf of a number of people?

Question Detail:

If a person has the capacity of sacrificing only one animal, can he sacrifice it for his parents, kids or wife? Or is it required for him to sacrifice one for himself and if he had the capacity to slaughter a second one only then he can do it on behalf of others?

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
Qurbani is wājib (obligatory) on every Muslim who is:
1)  of sound mind - mature (has reached the age of puberty), 
2)  Muqeem (i.e. he is not a Shar῾ī traveller)
3)  Possesses the amount of 612.36 grams of silver or wealth equivalent to that value which is in excess of one's basic needs and debts, on any of the three days of qurbāni. It is not necessary that this amount be in one's possession for a complete lunar year.[i]
Hence, if a person qualifies for all the criteria which necessitate qurbāni, he will have to perform it on behalf of himself.  A sheep, goat or ram can only be sacrificed on behalf of one person.  Likewise, a share in a camel, cow, bull or buffalo can only discharge the obligation of one person. [ii]   If he has surplus funds, he can perform qurbāni on behalf of other family members.[iii] 
If the husband for example only has sufficient funds to perform one qurbāni, then he will be obliged to perform his own qurbāni as it is wājib upon him.  If his wife meets the requirements of qurbāni, she will be obliged to pay herself unless someone else takes the responsibility to pay for her qurbāni.  If the husband has the financial capacity to perform a 2^nd qurbāni only then can he carry it out on behalf of others.[iv]    
 
And Allah Ta’āla Knows Best
Mawlana Faraz Ibn Adam,
Student Darul Iftaa
UK
 
Checked and Approved by,
Mufti Husain Kadodia.
www.daruliftaa.net