Popeye the Shih-Tzu Dog: Eye Problems of Our Canine Friend
Well, first off, let me state I am not a veterinarian but have had first-hand experience with Shih Tzus and eye problems. As to the general question about if squeezing a Shih Tzu's head will make its eyes pop out, that isn't too likely unless there was skull-crushing force which would have the same effect to you or me as well.
My first dog was a Shih Tzu. Her name was Meg. Since she is long deceased, there's no reason to protect her anonymity. She made the mistake one day of attempting to eat the food of my brother-in-law's dog. He had a springer spaniel and was visiting. His dog didn't seem to be into the sharing concept, especially since Meg never asked and ran over to Meg who fled under the nearest table and hit her head in the process. Unfortunately, the blow to her head was hard enough that one of her eyes dislodged from its socket, which is a common injury for Shih Tzus, as if their breed name wasn't misfortune enough.
Meg was immediately taken to the vet were the eye was restored as best as possible to its original resting place however she had little if any sight from that eye and it became clouded over much like it had a cataract. I was probably in the eighth grade at the time and there was quite a bit of blood at the time of the incident so it was a traumatic experience for both me and my dog and I obviously wished it hadn't happened but this is how I learned firsthand about this problem Shih Tzus and other similar breeds have.
Because Shih Tzus are a long-hairedÂ breed, they have long eyelashes which can cause problems with the lashes getting caught in the lid and irritating the eye. This is a relatively simple problem to correct. The Shar PeiÂ is also another breed that has numerous eye problems due to their breeding that can require many expensive surgeries. They don't have the "pop-eye" issues but they have problems with their eyelids. They can be quite sensitive to allergens and their eyelid folds can cause problems. The best advice is just to be aware of these issues and research any breed before purchasing so you know what you are in for.