A ringless web is configured to repair heart valve function in patients suffering from degenerative mitral valve regurgitation (DMR) or functional mitral valve regurgitation (FMR). In accordance with various embodiments, a ringless web can be anchored at one or more locations below the valve plane in the ventricle, such as at a papillary muscle, and one or more locations above the valve plane, such as in the valve annulus. A tensioning mechanism connecting the ringless web to one or more of the anchors can be used to adjust a tension of the web such that web restrains the leaflet to prevent prolapse by restricting leaflet motion to the coaptation zone and/or promotes natural coaptation of the valve leaflets.