They keep it until he animal is adopted, if it doesn't get adopted in this area they'll send it to another shelter. They will put the animal down if the animal is "not adoptable", meaning it is too aggressive with food, other animals and/ or people, but they do try to work with the animal first, putting it down is a LAST RESORT. Another reason is if the animal is badly injured and there is no chance in it surviving its injuries.
A reminder: if a shelter advertises " his time is running out" or something about he is running into problems or some other obtuse language about an animal its probably a kill shelter.
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