If you look at the original data in the Data Inspector, do you see anything at that first location?

What format is your source data? Any chance it might include "empty" objects around 0,0?

@redgeographics If i search in FME Inspector for the same line-object before use of lineonareaoverlayer-Transformer, this line could be find and zoomed. But after transformation this line-object (actually, part of this object) will be split through overlay of polygon and could not be find anymore. It hapends but not with all lines.

Source data is in shp-format. Think, there is no empty objects there.

If it wasn't shapefile I'd almost think it might be an arc centerpoint, but it is a shapfile so that probably rules out arcs.

Can you post your data and workspace here? That way it's easier to get a good idea of what's going on.

@redgeographics heyyy, sorry, it was FFS-file not shape. What do you mean about arc centerpoints? Will post my data here later.

Oh, in that case it might be an arc. You see, an arc segment is defined as a centerpoint with a radius (or 2 in case of an elliptical arc), start angle and sweep angle. If it's a very large radius the centerpoint might be very far outside your area of interest, but that's the only point that's actually stored in the file. CAD formats often have this.

You can try running your data through an ArcStroker, which will replace it with a series of straight line segments, then do the LineOnAreaOverlay.

Be sure to turn off the background map in the Data Inspector. Otherwise your data will be reprojected to match the background. I don't know if that's the problem, but it won't help.