Complex sentence: Neither disposition, age, nor illness affect whether a cat will be accepted to stay at the Refuge, and adoption is the ultimate goal, but unadoptable cats may live out their lives on the property as well.
Split into simpler sentences: Neither disposition, age, nor illness affect whether a cat will be accepted to stay at the Refuge. Adoption is the ultimate goal, but unadoptable cats may live out their lives on the property as well.