A saving throw—also called a save—represents an attempt to avoid or resist a threat. You normally make a saving throw only when a rule requires you to do so, but you can decide to fail the save without rolling. The result of a save is detailed in the effect that allowed it. If a target is forced to make a save and lacks the ability score used by it, the target automatically fails.
Page 373 of PHB 2024
Bolded section is what I am concerned with. Does this mean that if I am a Barbarian with Strength/Constitution saving throw proficiency, that I automatically fail when needing to perform a Dexterity saving throw (because I do not have the ability score used by it)? Example here would be the Fireball spell cast by an enemy.
By my reading, your hypothetical Barbarian does have a dexterity ability score whether or not they have proficiency in the saving throw. If they wanted to say lacks proficiency they would have said that directly. I’m not super familiar with the 2024 rules, so I don’t know under what circumstances a target might not have the ability score; maybe immobile objects don’t have dexterity?