Draw contour lines and fill right up to the fault line in Surfer

Surfer assigns NoData values to the grid cell when a fault BLN line crosses the cell, therefore the grid cells around the fault line will contain NoData values.

There is no way to prevent this without removing the fault data from the grid file. However, you can minimize the NoData area around the fault lines by decreasing the size of the grid cells (increasing the grid resolution). To do this, you can click Home | Grid Data | Grid Data and re-grid the data with the fault file, specifying smaller grid cells (increase the # of Nodes or decrease the Spacing in the Output page of the Grid Data dialog) or you can resample the grid file to a higher resolution.

Alternatively, you can increase the width of the fault line in the contour map to cover some of the NoData area. 

Updated December 6, 2021