They are not denied Saves.
Saves are not a Reaction, but a compulsory mechanic of the game wherein a creature must try to dodge, endure, or ignore an effect, depending on what has been cast. This is often the case with Area of Effect spells or abilities, whereas most physical, single-target attacks and abilities are usually made against a creature's Armor Class.
From the 5th Edition Player's Handbook:
A saving throw--also called a save--represents an attempt to resist a spell, a trap, a poison, a disease, or a similar threat. You don’t normally decide to make a saving throw; you are forced to make one because your character or monster is at risk of harm.
If a creature is Unconscious, however, they automatically fail their Strength of Dexterity Saving Throw.
From the 5th Edition Player's Handbook:
An unconscious creature is incapacitated, can't move or speak, and is unaware of its surroundings.
The creature drops whatever it's holding and falls prone.
The creature automatically fails Strength and Dexterity saving throws.
Attack rolls against the creature have advantage.
Any attack that hits the creature is a critical hit if the attacker is within 5 feet of the creature.
During each round of combat, a character is allotted one Action, one Interaction, Movement, and one Reaction. All but the Reaction must be used during that character's initiative in the combat. Reactions, however, may be used at any time during the round, so long as they have a valid trigger.
From the 5th Edition Player's Handbook:
Certain special abilities, spells, and situations allow you to take a special action called a reaction. A reaction is an instant response to a trigger of some kind, which can occur on your turn or on someone else's. The opportunity attack, described later in this chapter, is the most common type of reaction.
When you take a reaction, you can't take another one until the start of your next turn. If the reaction interrupts another creature's turn, that creature can continue its turn right after the reaction.