the sentence there is I know a diode can short out and fail closed. Is it possible for a diode to fail in the open position, and what would cause this to happen?
"a diode can short out and fail closed" is just expressing the same thing two ways. The diode fails so that it acts like a wire (aka short circuit aka closed switch).
A diode that fails short (aka closed) is likely to turn into an open if enough current is available to damage it further.