“Dark Cat With White Tail”’s effect targets, so the targets are chosen at activation of its effect.
If “Ring of Destruction” is chained to “Dark Cat With White Tail”’s effect, and destroys some of the selected monsters, or destroys the cat itself, the cat’s effect still resolves as normal.
To activate “Dark Cat With White Tail”’s effect, there must be a minimum of 2 monsters on your opponent’s side of the field and a minimum of 1 monster on your side of the field.
When “Dark Cat With White Tail” is attacked, flipped, and destroyed by an attack, you cannot select the cat itself for its effect so if the cat was your only monster, the cat’s effect is not applied.
Netrep Rulings:
The Flip Effect of “Dark Cat with White Tail” is not optional. If there are not enough monsters on the respective fields to satisfy “Dark Cat with White Tail’s” effect, “Dark Cat with White Tail’s” effect disappears.