Nothing, apparently.
I’ll spare you the details, but will provide them if necessary. Last week my MetroCard fell out of my shirt pocket and into the toilet at work. I flushed it away, along with the $22 balance it carried and the other contents of the bowl. When I told my friend about the incident, he told me that it might cause some clogging issues in the building.
So far, as far as I know, nothing bad has happened.