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Can someone tell me how to dash a part of a region where the function doesn´t exist?

An example 1 >= x^2 + x > y, where y is not included.

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You can use ContourPlot with x^2 + x == y as the first argument and use it first Part as Epilog in RegionPlot:

 RegionPlot[1 >= x^2 + x > y, {x, 0, 1}, {y, 0, 1}, 
  PlotStyle -> Opacity[.1, Blue],
  PlotPoints -> 100, BoundaryStyle -> None,
  Epilog -> ContourPlot[ x^2 + x == y, {x, 0, 1}, {y, 0, 1}, 
    ContourStyle -> Directive[Thick, Red, Dashed]][[1]]]

enter image description here

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