Is it possible for a creature like a bear to make an attack that counts as an unarmed attack, even though it has a claw attack as a Natural Weapon?
Yes. A non-monk bear without Improved Unarmed Attack could throw a punch, and that would be an unarmed attack that used the typical unarmed attack values for a creature of the bear’s size, be nonlethal, and provoke attacks of opportunity. Because a punch “uses” the bear’s paw, doing so prevents the bear from using his claw attack. He may still use his bite attack, but at a −5 penalty.
It can reasonably be assumed that a wild bear would never do so, but it could, and more relevantly someone shapeshifted into a bear could and might even want to do so, particularly if that person had Improved Unarmed Strike to eliminate the AoO provoking.
If a bear was also a monk (or, again, more realistically: a monk turned into a bear), the bear’s unarmed strike damage would deal damage as appropriate for a creature of the bear’s size with the given number of monk levels. Moreover, the unarmed strike would not need to be a punch (e.g. a kick), allowing the bear to also use his claws (again, at a −5 penalty).
Some relevant information about monks with natural attacks:
Basically, claw attacks are, well, attack with claws. Usually, the "unarmed combat" term refers to "punching stuff with your fists", and bear may as well do it, through, it surely does not posess an "Improved Unarmed Fighting", so if you want to optimize it a bit, you may give your bear a 1-level monk dip:
Basically, this text grants us two pieces of knowledge:
okay, basically it's just a post about monk bears now XD
While you already accepted an answer, I'd still give another.
It is true no rules as i know directly forbid unarmed strikes on a bear or the like. On the other hand, there is no direct statements to ensure one that animals can fight unarmed (even someone shifted or transmuted into an animal).
I'd personaly rule against unarmed strikes on a bear.
Brief clarifications on my point of view on animals and grapple:
There are two "types" of animals from the viewpoint of grappling: some hasn't Improved Grab and some has. First ones normally will not try to start a grapple and if they are grappled will try to byte or scratch you (i.e. attack with natural weapon with -4 penalty). Those who has Improved Grab use their natural weapon's (which the creature used to establish the hold) damage in place of unarmed strike damage. They also has previous option, of course, but will use it quite seldom, i think.
What about someone who "became" an animal by some means? Most common ways to do so are Alternate Form and Alter Self and their variants.
Alternate Form says:
Alter Self says:
Unarmed strike is a natural weapon (with some special rules, but still it is). So I think you lose it, when you polymorphed/wildshaped into something that hasn't it.