The tears will evaporate over time just as on Earth. However if there is some kind of irritants in a space suit, something which have happened a few times, then the astronaut will produce more tears then will evaporate and there is no way to wipe the tears away. So the tears will pool up around the eye making them blind. It will then cross over the nose to the other eye covering that as well. Eventually it will pool down to the nose and the astronaut can drown.
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