This is happening in Poser6. Set the character up with mats and INJ's and everything... when you open up a pose library and apply a pose, any pose, from any package - this is what happens.

I'm really stumped.

It happens all the time, it's nothing unusual.  Just readjust each eye's x, y, & z trans, usually by a value of 0.001 or 0.002.  x trans have to mirror each other, so one might need to be set at, say 0.001, while the other at -0.001.
It's a simple enough thing to correct.
Hoadley

Yes, I've had that occasionally.  I just select the eyeball and move it back into the head a bit using the parameter dials.

Ah  cool, just never seen it before..

Thanx for clearing it up for me :)

"happens all the time?"

I've never ever seen this before. It looks spooky...
What happens when you render it? Does the eyes pop back in place? In that case it MIGHT be a OpenGL issue, I've heard people complain about them...

This is a render .. so this is pretty much it

I've had it happen with both eyes and teeth in underedered before.. but not staying like this

This can happen when morphing the face to create a character, which INJ poses are -morphs to create character.  In this case, it's obvious that the facial features have been flattened to a degree that the outer skin is further back that the outer edge of the eyeball.  Just readjust the eyeball's transet parameters to fit the new location of the eyesocket. 
It's no big deal, when I create characters in Eve 4, I have to readjust the spatial location of the eyeballs to coincide with changes in my characters newly wrought faces.
David P. Hoadley

That's the odd thing tho..  it's not me this is happening to..it's one of my customers..

and everybody else I know of with this character has no problems with this.. It's just odd that it's happening to one person, and not everybody.. 

Any ideas why it's happening?

I do hope it's not the character, but if it is I want to be able to fix it somehow

Have him do an EditRestoreFigure first, plus a Joint ParametersZero Figure, and see if the figure remains in default.  There may be some morph values embedded in the Figures Cr2.  This happened to me once.  No matter How many times i did an Edit/Restore, it defaulted to a previously morphed figure.  I finally had to manually edit the Cr2  to eliminate the hidden morph values.  It wasn't a fun experience, but if all else fails, you may have to do that.
David P. Hoadley