## The rules don't say

The rules neither allow nor deny such a species as a firbolg/elf hybrid (or "race", using the 2014 term).

## There is no such playable species (or race)

. . . in any version of D&D.

## There's *probably* no such NPC

There does not *seem* to be any such NPC, at least in my experience, but hard to prove a negative.

## But a DM can decide differently

The rules **explicitly** allow the DM to create races, see the DMG, ["Creating a Race or Subrace"][1].

## It's a question of narrative, not biology

There's absolutely zero reason to consider biology the limiting factor here.  First of all, fantasy role-playing game: if a DM thinks a firbolg-elf (or elf-firbolg, or for that matter, any combination of species) would be fun, then the DM should not feel constrained by the rules.

We left biology behind on the first page.  And an elf-firbolg combination is certainly no more preposterous than a fiend/human or fiend/anything combination.

The DM would just need to come up with the narrative to justify the interbreeding to whatever extent they felt it needed justification.  And in a game with celestial and infernal beings, floating castles, unicorns, etc etc, interbreeding between an elf and a firbolg is small potatoes.  If the biology bothers you, maybe they were combined by magic.


  [1]: https://www.dndbeyond.com/sources/dnd/dmg-2014/dungeon-masters-workshop#CreatingaRaceorSubrace