I find it pretty sad that hardly any of the fighting styles work for a Dhampir who wants to primarily use their fangs…

Whilst I am happy to hand wave that Duelling or Unarmed Fighting Style SHOULD apply in terms of game balance and opportunity cost… the language makes it clear that they don’t. So I was thinking of making one:

Feral Fighting Style

Your natural weapons’ damage die becomes a d8. While you are missing half or more of your hit points, the d8 becomes a d10.

 (I say d8 and d10 because most natural weapons are now d6s and each increase in damage die is only an average of 1 extra damage, whereas Unarmed Fighting increases unarmed strikes by a significant margin, even if it would generally be 1 damage less than this... if both had a shield)

Relative increase isn't the meaningful statistic, the game balance is designed around Defense vs Damage. Hence 2-handed weapons always do more damage than 1-handed weapons since one-handed weapons let you use a shield at the same time boosting your AC vs the 2-handed weapon user. Similarly among 2-handed weapons, weapons with Reach deal less damage than those without it since having reach allows you to attack and back away without taking an AoO (reducing your risk of getting hit).

@Agilemind So I take it that is one vote towards it being a d6 and then a d8, rather than d8 and then d10? Which sadly would have the side effect of making this homebrew Fighting Style useless for the majority of races with a natural weapon.

I could add that you cannot use a shield though, like with Unarmed?

 Edit: How about about scaling with proficiency? Say double the proficinecy bonus? so...

• lv1-4 d4
• lv5-8 d6
• lv9-12 d8
• lv12-16 d10
• lv17-20 d12

To keep up with a 'feral' theme this could come with a restriction against wielding weapons or shields and still have a half-health feature... that say doubles the dice. So that it could be 2d4 at lv1 and 2d12 at lv17, what do you think?

 Edit 2: Another few options, stolen from the Lycan Bloodhunter, Champion or Vampire statblock

1. When you use the Attack action to attack with a natural weapon, you can make one additional natural weapon attack as a bonus action.
2. At the start of each of your turns, you regain hit points equal to 1+ your Constitution modifier (minimum 1) if you have no more than half of your hit points left. You don’t gain this benefit if you have 0 hit points.
3. When you are missing half or more of your hit points, gain resistance to Bludgeoning, Piercing, and Slashing from Nonmagical Attacks

For example:

Feral Fighting Style

You can roll a d6 in place of the normal damage of your natural weapons. When you are missing half or more of your hit points, this become 2d6 instead and you gain resistance to Bludgeoning, Piercing, and Slashing from Nonmagical Attacks.

Why do you want a single FS to do all of that? Lycan Bloodhunter is a whole subclass, Beast Barbarian is a whole subclass. 

If you have a Damphir who wants to use their fangs I'd suggest encouraging them to pick one of those subclasses and HB ruling that they can use their Fangs as the natural weapons granted by that subclass. Alternatively suggest they choose Shadow Monk as shadow monk is by far the most vampire-y subclass available and then rule that their Fangs count as unarmed strikes.

Fighting Style useless for the majority of races with a natural weapon.

Oh you're now trying to make a Fighting style for all races with natural weapons? Why not instead use this HB rule:

Any natural weapons that are attached to limbs - e.g. claws / hooves - deal 1d4 or 1d6 damage and are considered "Light" melee weapons and can be used for Two-weapon fighting and benefit from the two-weapon fighting fighting style.

Any natural weapons that are attached to a head, body or tail - e.g. teeth, fangs, horns, stinger - deal 1d6 or 1d8 damage and qualify for the Dueling fighting style.

Quote from Agilemind>>

Any natural weapons that are attached to limbs - e.g. claws / hooves - and deal 1d4 or 1d6 damage are considered "Light" melee weapons and can be used for Two-weapon fighting and benefit from the two-weapon fighting fighting style.

Any natural weapons that are attached to a head, body or tail - e.g. teeth, fangs, horns, stinger - deal 1d6 or 1d8 damage and qualify for the Dueling fighting style.

That sounds great, whose HB rule is that?

Quote from Cheeky_Hamster >>

Quote from Agilemind>>

Any natural weapons that are attached to limbs - e.g. claws / hooves - and deal 1d4 or 1d6 damage are considered "Light" melee weapons and can be used for Two-weapon fighting and benefit from the two-weapon fighting fighting style.

Any natural weapons that are attached to a head, body or tail - e.g. teeth, fangs, horns, stinger - deal 1d6 or 1d8 damage and qualify for the Dueling fighting style.

That sounds great, whose HB rule is that?

 It's just mine, I also let spells that target "a weapon you are holding/touching" to target natural weapons as well, and artificer to use infusions on natural weapons. I did a similar thing for Battlerager spikes on their armour so they can get +1 spikes / +2 spikes as magic items.

Nice, I like that!

I might have my player’s damage die go up as a boon from Strahd rather than using the Fighting Style