Why would a blood vessel in the eye break without any trauma to the eye?

Many causes: Subconjunctival hemorrhages are common vessels on the white of the eye that break due to age, trauma, high blood pressure, valsalva, anticoagulants, etc. Blood vessels inside the eye can also bleed due to conditions such as diabetes, hypertension, ocular ischemia, etc. Thus many causes.

Blood vessel: Blood vessels on the surface of the eye break due to coughing, sneezing, straining. This is called subconjunctival hemorrhage, and is a benign condition. Blood vessels inside the eye may break due to diabetes, high blood pressure, lupus, sarcoidosis, sickle cell, hiv, etc.