I played Sigilyph online and ran into this exact situation (and it was Blacephelon who KO'd me. Ha!) Going into the final attack from my opponent, we each had two prizes remaining.
After Blacephelon's attack (200 damage), we each had zero prizes, and PTCGO shuffled both of our decks, dealt out a new game, except we each had one prize. So it was a one prize race/overtime. And a new coin flip to see who goes first.
Hillariously, in that same match and overtime, the same thing happened - my opponent KO'd my active Sigilyph again. So PTCGO reshuffled and reset with one prize each.
(Then my opponent won in double OT.)
It's also important to note that the GX counter reset each time. My plan for a quick overtime win was to snipe a little basic on his bench with Espeon's GX, and with the reshuffle/reset, this was possible. (Just never drew an Eevee - go figure.)
It turns out that in a one prize overtime, luck of the draw is VERY important.