TechSmith's SnagIt has this feature. They call it, "cut out". Their description is better than mine, "Delete vertical or horizontal sections out of an image and join the two pieces together."
Basically, there are 2 main aspects of this functionality...
You select either a direction [vertical or horizontal] and style [abrupt, fade, or tear].
You select a starting point and an endpoint that goes top-to-bottom [for vertical] or left-to-right [for horizontal]. On the selection of the second-click [endpoint], the entire selected region is cropped. The "edges" are styled and the cut out is removed.
BEFORE: XXXXXZZZZZXXXXXX where ZZZZZ is to be "cut out"
AFTER: XXXXX| |XXXXX and | | marks edges which may be "sharp", gradient fade, or zig-zag tear. Not the reduction in space from ZZZZZ to | |.
I found to explain the UI.
-Jason