If you select Keep Islands =No then if the gap into an area is less than the clearance set in the Design Rules then the copper area cannot connect into that area.
If you select Keep Islands =Yes then the areas will fill with copper but they will not be connected to anything. However, having floating areas of copper is not good practice as it can cause crosstalk and other problems.
If you want to fill the cut off areas then consider adding extra vias tracked in from the other side of the board.
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