unadoptable

/ˌʌnəˈdɑptəbəl/
adjective
  1. Not suitable or eligible to be adopted, especially of a pet or child.
    • They hoped to find a home for every animal, but some were considered unadoptable due to age.
    • The shelter said the dog was unadoptable because of its severe health issues.
    • The rescue group worked with unadoptable cats to improve their behavior.
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