How possible is it to rip someone's eye out of its socket?

Being a nurse, I am in the unique position to ask a surgeon this question.

The answer is: YES. This is entirely possible according to a surgeon that works at the same hospital that I do. With enough force, this can be achieved.

It is possible to pop the eye out of the socket and get it caught between the lids. this is called Exophthalmos. This can damage the eye unless it is put back into place.

There are also cases of mentally ill individuals that actually stick their fingers through the tissues over the eye and pulled their own eyeball out of the socket. This is called Self-enucleation.

In this particular case, where eye gouging is used for self-defense, YES this is possible as well.

Rather you should try to force your thumb between the eye socket and the eyeball into the skull. This will cause more pain, more fear and continued, increasing pressure will either destroy the eyeball or pop it out of the skull.

The following article explains an actual attack that resulted in a man gouging out the eye of another man:

A man whose eye was gouged out by a random assault, according to police, is shocked and angry that his attacker is already back on the street. He went through the eyeball I can’t describe to you the pain.

As a student of martial arts and complex anatomy, I can confirm this as well.

In what the Shaolin call "iron body" training, the bones of the fingers and hand can be made profoundly dense. This is a systematic process called 'micro-trauma ossification'. By striking dense materials such as kidney beans, sand and iron shavings, in that order from lowest density to highest, the normally fragile bones of the hands become denser. Micro-trauma ossification occurs with each strike.

So long as the hand is able to rest and recover, the series of strikes causes tiny fractures in the bones at the cellular level, known as the 'bone matrix'. This latticework material increases in density when the surrounding muscles hoist heavy weights, or in this case, when the bone is subjected to trauma. Each time the area is traumatized, at a cellular level, the bone matrix's gaps become smaller and can vanish in extreme cases. Martial artists such as the Shaolin are the extreme and their bone matrix is incredibly dense. Because of this, their hands alone can accomplish amazing feats of strength.

The eye itself is comprised of soft tissue, lubricative fluids and water. The retina is a nerve bundle but through cranial trauma, it can become detached from the eyeball. In stark contrast to the eye and its retina, the eye socket is made of hard tissue: bone. When a dense martial artist's finger (such a Kiddo's fingers in 'kill bill') comes in contact with a soft, lubricated eyeball, it recoils into the socket. An exchange of physical forces occurs here.

Due to the dense bone and quick recoil of the eye, it can be grabbed from within the hard eye socket. Pulling it out is tricky; the eye is constantly lubricated in fluid, for eye rotation, as is the socket's surrounding tissues. The eye will instantly produce tears and if squeezed too hard, it will bleed or slip out of the attacker's fingers. The retina is bound to resist a quick pull, but in the case of a strong, dense set of quick fingers, the retina is unable to resist and is compromised. The attacker holds an eyeball, with bloody retina attached to its rear surface and the victim is blinded on one side.

Martial arts, at its core, is a combination of physical sciences, precisely performed, on a human body. Not only is an eye-snatching maneuver possible, masters of martial arts can break concrete with their bare hands. In truth, not all of martial arts is "movie magic". Even a career boxer's dense digits, when curled into a fist, can shatter the bones of an ordinary man's face in multiple places.