Ruling on killing of dogs that eat the sheep
Question

                In my community there are some Muslims who are rearing sheep. they send them out to graze in the pasture all day with no one looking after them. sometimes they get attacked by dogs and are eaten. the owners then go and try to catch the dogs and kill them. so i would like to know if it is allowed islamically for these dogs to be killed? shouldnt there be someone guarding the sheep to prevent dogs from attacking?.
Praise be to Allah.
      Firstly: 

    It is by the mercy of Allah, may He be exalted, to His slaves 
    that He has created for them what is in the heavens and on earth, and He has 
    subjugated it in their interests, for their livelihood. Included in that is 
    the fact that He has prescribed for them to ward off harm and aggression 
    from themselves and their property or wealth, even if that leads to killing 
    the aggressor or the one who is causing harm to them, such as wolves or 
    other predators. But with regard to animals that do not cause harm, it is 
    not permissible to kill them. 

    See: al-Mughni, by Ibn Qudaamah, 4/324 

    Secondly: 

    Dogs are of two types: those which it is Sunnah to kill and 
    those which are not to be killed. As for those which it is Sunnah to kill, 
    it is the black dog because it is a devil, and the vicious dog because it is 
    harmful. All other dogs are not to be killed. 

    If these dogs are attacking the sheep and killing and eating 
    some of them, then these are harmful dogs whose harm is to be warded off 
    even if that is by killing them; rather they should be killed because of the 
    mischief that they are causing. Al-Bukhaari (1829) and Muslim (1198) 
    narrated that ‘Aa’ishah (may Allah be pleased with her) said: I heard the 
    Messenger of Allah (blessings and peace of Allah be upon him) say: “There 
    are four (creatures), all of which are vermin and may be killed inside the 
    sanctuary and outside: kites, crows, rats and vicious dogs.” 

    The scholars of the Standing Committee said: 

    With regard to dogs that are harmful because they are vicious 
    or are predators or have rabies, and other kinds of aggression and fearful 
    matters, there is nothing wrong with killing them in ways that do not cause 
    harm to others that are not harmful. End quote from Fataawa al-Lajnah al-Daa’imah, 
    26/201 

    The scholars of the Committee were asked: 

    One day I caught a dog that had attacked one of the sheep but 
    not killed it, and I killed this dog. Please note that I do not know who 
    this flock belonged to; I carried the sheep and put it in a fenced area 
    nearby and left it there. 

    They replied:

    If the situation was as you describe, then what you did was 
    good and there is no blame on you, because you saved the property of your 
    Muslim brother from being destroyed and you will be rewarded for that, in 
    sha Allah.

    End quote from Fataawa al-Lajnah al-Daa’imah, 26/205 

    There is no doubt that it is worthwhile for the owner of the 
    sheep to appoint someone to guard them or a shepherd to look after them, but 
    that does not mean that it is not prescribed to kill these dogs, because 
    they have got used to attacking and if they fail to catch one thing they 
    will look for something else and attack it. Hence it is prescribed to kill 
    them. 

    So these dogs are to be killed and the owner of the sheep 
    should be instructed to look after them and protect them. 

    And Allah knows best.