How a fragment is combined with the data already in the frame buffer depends on various settings. In a typical case, a fragment may be discarded if it is farther away than the pixel that is already at that location (according to the depth buffer).
The process of integrating a fragment into the already present data within the frame buffer depends on various parameters. Usually, a fragment could be removed if it is positioned further from the current pixel in the scene (as determined by the depth buffer).