unadoptable

adj

1. That cannot be adopted; unsuitable for adoption.

   “Even children with minor or correctable handicaps such as harelip, cleft palate, crossed eyes, or clubfoot were classed as "unadoptable".”

   “At Columbia-Greene, staffers go for the most unadoptable animals to save them from euthanasia. The youngest, healthiest, cutest pets are waiting for you.”