An apparatus for treating a wound with negative pressure wound therapy, comprising: a stabilizing structure for insertion into or over a wound, the stabilizing structure configured to collapse under negative pressure, the stabilizing structure having a length extending along a central longitudinal axis of the stabilizing structure, a width transverse to the length extending along a central transverse axis of the stabilizing structure, and a thickness transverse to the length and the width, wherein the length and width are greater than the thickness, and wherein the stabilizing structure comprises: a first side and a second side extending the length of the stabilizing structure, and a third side and a fourth side extending the width of the stabilizing structure, wherein the first side is opposite the second side and the third side is opposite the fourth side, and wherein the first side and the second side are curved or bent outwardly relative to the central longitudinal axis to provide an outer perimeter of the stabilizing structure with an at least partially elliptical shape; a plurality of elongate strips extending the length of the stabilizing structure from the third side to the fourth side, wherein the plurality of elongate strips comprise outermost elongate strips defining the first and second sides of the stabilizing structure and a plurality of inner elongate strips positioned between the outermost elongate strips; a plurality of intervening members connecting the elongate strips, wherein the plurality of intervening members are configured to pivot relative to the strips to allow the plurality of elongate strips to collapse relative to one another; a plurality of cells provided side-by-side in a horizontal plane parallel to the length and width of the stabilizing structure, each cell defined by a plurality of walls extending in a vertical direction perpendicular to the horizontal plane and formed by either the elongate strips or the intervening members, each cell having a top end and a bottom end with an opening extending through the top and bottom ends; wherein the lengths of the cells along an elongate strip are progressively longer toward the central transverse axis; and wherein the stabilizing structure is configured to collapse more in the horizontal plane than in the vertical direction by collapsing the plurality of cells. a first side and a second side extending the length of the stabilizing structure, and a third side and a fourth side extending the width of the stabilizing structure, wherein the first side is opposite the second side and the third side is opposite the fourth side, and wherein the first side and the second side are curved or bent outwardly relative to the central longitudinal axis to provide an outer perimeter of the stabilizing structure with an at least partially elliptical shape; a plurality of elongate strips extending the length of the stabilizing structure from the third side to the fourth side, wherein the plurality of elongate strips comprise outermost elongate strips defining the first and second sides of the stabilizing structure and a plurality of inner elongate strips positioned between the outermost elongate strips; a plurality of intervening members connecting the elongate strips, wherein the plurality of intervening members are configured to pivot relative to the strips to allow the plurality of elongate strips to collapse relative to one another; a plurality of cells provided side-by-side in a horizontal plane parallel to the length and width of the stabilizing structure, each cell defined by a plurality of walls extending in a vertical direction perpendicular to the horizontal plane and formed by either the elongate strips or the intervening members, each cell having a top end and a bottom end with an opening extending through the top and bottom ends; wherein the lengths of the cells along an elongate strip are progressively longer toward the central transverse axis; and wherein the stabilizing structure is configured to collapse more in the horizontal plane than in the vertical direction by collapsing the plurality of cells.