If it's the 'stuff' inside the display it should be contained into the panel, so even if it 'bleeds' it should still be inside the panel. Unless it actually broke and it's leaking inside, but I think that would have caused a lot more major issues and chances are your phone wouldn't be turned on right now, or at least it'd be giving out smoke or 'burnt' odors.
Also, by panel I mean the AMOLED display panel, not just the glass on top. You might also have to replace the touch sensor if they're soldered together.