So there's a bit of a crazy theory circulating around the Intertubes that the Songbird's death in BioShock Infinite can actually be heard in the original BioShock game, while you're in Fort Frolic. Watch the video to hear it for yourself.
Obviously, it's a bit of a stretch to think they'd planned this out while BioShock 2007 was still in development, as Infinite's ending would have to be plotted out, too...but still very cool to imagine it's deliberate, and Ken Levine really is a mad genius.
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I dunno, that's a really faint and obscure sound. What seems more likely than them planning Bioshock Infinite is they maybe had some audio glitch making that sound, and they made the Songbird imitate the glitch in order to mess with people.