Eyelash extensions are pretty safe and usually not many people have any problems when they get eyelash extensions installed but there are a few risks associated with eyelash extension such as infection of the cornea, swollen eyelids, infection of your eyelids and even sometimes temporary loss or even permanent loss of your natural eyelashes.
Also in some rare cases if the glue used to put the eyelash extensions on gets into your eye you could go blind from the eyelash extensions but that doesn't happen often as long as your eyes stay closed during the procedure which they should.