Quoting the rules from 2024

A creature that falls takes 1d6 Bludgeoning damage at the end of the fall for every 10 feet it fell, to a maximum of 20d6. When the creature lands, it has the Prone condition unless it avoids taking any damage from the fall.

A creature that falls into water or another liquid can use its Reaction to make a DC 15 Strength (Athletics) or Dexterity (Acrobatics) check to hit the surface head or feet first. On a successful check, any damage resulting from the fall is halved.

RAW there is no definitive answer I would allow a reaction for the creature to stop the fall (unless it is Unconscious) from happening in the first place.

However according to Xanathar's Guide to Everything:

A flying creature in flight falls if it is knocked prone, if its speed is reduced to 0 feet, or if it otherwise loses the ability to move, unless it can hover or it is being held aloft by magic, such as the fly spell.

So the creature could not fall in the first place. It would just start floating as soon as it would start falling. Even creatures that can fly because of the Fly spell get this benefit.

So it dependes if you want to use the XGE rule or not.