"Clementine will remember that" - Telltale's The Walking Dead adventure game
Within the fictive world of our Dungeons and Dragons game, when we establish that consequences come of player decisions and character actions we create a short emotional engagement loop: Action begets Reaction, Failure begets Consequence. Between the two is a possibility space, which players fill with emotional anticipation of the consequence. Playing with this space is a skill, well executed by those for whom consequences come at a time other than immediately after the choice is made. Telltale Games (of The Walking Dead, Tales from the Borderlands to name two) are the absolute masters of this, along with our oft-quoted mentors of Failbetter Games (Sunless Sea, Fallen London).
A Pocketful of Punishment
In a situation where a failure state is suggested, but not clear, deferring the consequence helps to drag out that scary, unknowing feeling. For example, when a character is struck by a noxious gas and fails their Constitution Save, their player immediately processes some degree of fear. They have failed, so they know that something bad is going to happen. Maybe they check off possibilities in their head. Poisoning? Sleep Gas? Disease? Curse? What if it's a gas that eats away at their armour, or other resource they’re not content to lose?! At some point in this horrified thought process the DM will step in: "You are poisoned." And the horror slips away, replaced by the planning phase on how they'll move forward. If you, as a DM, don't tell them initially ("Something rests in your stomach, you feel the lump it leaves, but you won't suffer any mechanical effects...today.") you can extend and maintain the implied threat. My personal favourite is to tell them "I'll give you what you want, and you succeed, but I'll keep that failure in my back pocket for later."
Tools to Take Away
Deferred Consequences allow DMs to both extend the emotional curve of failure, and also to ensure the consequence comes at the most narratively and mechanically effective moment. You need to ensure the player knows when both the consequence is deferred, and when it is brought back into play. Sunless Sea is required reading here. They present an underspecified line after a choice is made: “Something has changed in the ‘Neath”. This gives authority to defer (and gives players space to imagine). Then, when the consequence is initiated, they state “You did X, therefore[...]”. This links the consequence to the choice, giving authority to execute the consequence. An example in tabletop RPG mechanics is Apocalypse World’s Read a Sitch move which states “On a miss, ask [a question of the MC] anyway, but be prepared for the worst.” The outcome of the failure is uncertain (underspecified threat), and the MC gives truthful answer. These answers may be consequential themselves (hard moves, immediate consequence), or they may simply set up a situation on which to execute the consequence later (soft moves, defering). Importantly, as former Failbetter CEO Alexis Kennedy said: "The game is what happens inside your player's head [...] if they don't realise a consequence is a consequence, it might not as well have been a consequence."