I am using ArcMap 10.1 and am trying to create a legend that will display a polygon layer as a single line.
Decrease the height of the the legend box to zero: In the example below you can see that I got a line legend even if my data is polygon. Right-click on your legend, click on properties Go to the Legend tab and change the height into either 1 or 0.
That will reduce all polygon layer patches in the legend to lines. You can also set this property per-layer, by bringing up the Legend Item Properties for the layer (double-click the layer under the Items tab). Then check "Override default patch size" and make the same change:
The workaround I usually use for any situation in which I want to customize the legend entry for a layer is to create a dummy layer which is only used in the legend, and not displayed on the map. So in your case, create a new line layer using a line shapefile with no features in it, symbolize it however you want, and add that to your legend. The new layer should be turned off in the map. You will need to uncheck the box "Only display layers that are checked on in the Table of Contents" under the legend properties.