How does 'damage your opponent' work with natural attacks?

[Dracuwulf]

Damage Your Opponent: While grappling, you can deal damage to your opponent equivalent to an unarmed strike. Make an opposed grapple check in place of an attack. If you win, you deal nonlethal damage as normal for your unarmed strike (1d3 points for Medium attackers or 1d2 points for Small attackers, plus Strength modifiers). If you want to deal lethal damage, you take a –4 penalty on your grapple check.

How does this work for creatures with natural weapons?

 

[Patryn of Elvenshae]

How does this work for creatures with natural weapons?

Generally, it doesn't.

They may make grapple checks, as above, to do damage as an unarmed strike for a creature of their size (1d3 for medium creatures, etc.).

*OR* they may use the "Attack Your Opponent" option, in place of a normal attack. Note that many creatures with a natural attack who will grapple often will have special grappling abilities, like Constrict or Rake.

Attack Your Opponent: You can make an attack with an unarmed strike, natural weapon, or light weapon against another character you are grappling. You take a –4 penalty on such attacks.

You can’t attack with two weapons while grappling, even if both are light weapons.

Note that due to the text preceding this section -

If your base attack bonus allows you multiple attacks, you can attempt one of these actions in place of each of your attacks, but at successively lower base attack bonuses.

- any creature attacking with a natural weapon is limited to a single attack, since natural weapons never give iterative attacks based on BAB.