Can a Bard’s Superior Inspiration be used on the initative roll that generated it

The GM must reveal the number on the die

Whenever a player has an ability to do something after knowing "the roll, but not the result", the GM must either tell or show the player the number on the dice, as confirmed in this pair of unofficial tweets from June 2016 by rules designer Jeremy Crawford:

Bard Combat Inspiration use with reaction to add the roll to AC "AFTER SEEING THE ROLL" So DM must show his roll to player?

If a player character ability relies on knowing a monster's roll, a DM may say what the roll is or show it

Master @JeremyECrawford, you intended that DM must communicate only the number on the dice (without added any modifiers), right?

That's correct.

Relevant modifiers or target numbers do not have to be revealed, only the raw rolls of the dice.

Therefore, it is courteous and convenient for the GM to roll the dice openly whenever there is a chance for a player to use their inspiration, ask whether the player wants to use their inspiration, and declare the hit/miss after the player replies.

Nothing, it's still there.

Long story short, there's nothing in the rules for Bardic Inspiration that says it goes away if either the giver or the recipient is rendered unconscious or slain. One of the core rules is "Specific Beats General", and in this case, there is no General that says the dice would go away. There's nothing RAW stopping you from being slain, raised by a quick Revivify, and still having the dice.

And if you need an explanation for why you are still inspired by the bard you just saw turned into a pointy metal object repository, their words and music inspired you so much you're now doubly moved to avenge them.