Frankie was a teeny Yorkshire terrier that I groomed for years. As he got older, he developed a problem with discharge from his eyes. His owner brought him to me every twelve weeks to be shaved from nose to toes (we did leave funny fluffs on the tips of his ears as his trademark), and all was well. Until it wasn't. Let me explain.
Frankie would not allow his owner to clear the discharge that came from the tear ducts at the inner corners of his eyes (he was small but fierce), so by the time he came in for grooming, he would have an impressive build-up of hard, dark, dried yuck under each eye. When the problem began, I could aim a gentle stream of lukewarm water at the build-up during the bath and loosen the crust enough to wipe it away with his towel. But it got worse over time. The owner took him to the veterinarian, who prescribed medicated eye drops, but Frankie didn't like them, and his owner rarely managed to get them in. The eye drainage trapped moisture against his skin, so soon sores developed there, and if you think any of this made Frankie easier to deal with, please think again.
Dogs may have eye drainage for a variety of reasons. A little build-up in the eye corners, especially in the morning, is common for many dogs. Allergies, eyelashes rubbing on the eye's surface, lack of tear production (dry eye), and various other disorders can cause excessive drainage. Any of these are symptoms that a veterinarian should see.
As a groomer, you will ideally check for signs of irritated eyes and drainage when the dog is admitted for service. A conversation with the owner pointing out what you observe is important because when the discharge is washed away, the skin under the eyes will often be sore, red, and possibly infected. Photos of the crust before and after it is removed can also be helpful if there is any question of the owner potentially blaming the sores on the grooming process.
Gently soaking the discharge during the bathing process helps; sometimes, a fine-toothed comb can help lift it up and away from the face. If the skin beneath is irritated, flush it with cool water and try to trim away any hair that might get trapped in that area. As always, point out any abnormalities you find to the pet owner.
In Frankie's case, his refusal to allow his human to treat his eye condition and the pain it caused him shortened his lifespan considerably. I still miss the little guy.