When I do eye lining, I only work on half the eye at a time, with the client looking away from my machine, so I never work directly across the cornea. I think most experienced technicians would do the same thing. If you were to get a corneal abrasion, your eye would tear, swell shut within the hour, feel like you have sand in the eye, and be quite painful for a day or two. You should be sent to an ophthalmologist for examination, and would probably have antibiotic eye drops prescribed along with an eye patch. But the good news is that the condition usually heals itself within three days, and should have no long term affect on your vision.
Corneal abrasions are extremely rare, and are no reason to avoid the procedure.
But it is important to understand the risk, and be psychologically prepared in the unlikely event of a problem. Any technician who tells you the procedure is entirely without risk is probably not to be trusted. There is another eye lining risk which is easily avoided. Because of the anatomy of the eye, the technician should not tattoo in the outer corner between the lashes to join them together, or you run a significant risk of pigment fanning. That is where pigment will travel under the skin and appear beneath the eye as a bluish shadow.