The nearby young star beta Pictoris hosts a rich and complex planetary system, with at least two giant planets and a nearly edge-on debris disk that contains several dynamical subpopulations of planetesimals. While the inner ranges of the debris disk have been studied extensively, less information is known about the outer, fainter parts of the disk. Here we present an analysis of archival FORS V -band imaging data from 2003-2004, which have previously not been explored scientifically because the halo substructure of the bright stellar point spread function is complex. Through a high-contrast scheme based on angular differential imaging, with a forward-modelling approach to mitigate self-subtraction, we produced the deepest imaging yet for the outer range of the beta Pic disk, and extracted its morphological characteristics. A brightness asymmetry between the two arms of the edge-on disk, which was previously noted in the inner disk, is even more pronounced at larger angular separations, reaching a factor similar to 10 around 1000 AU. Approaching 2000 AU, the brighter arm is visible at a surface brightness of 27-28 mag arcsec(-2). Much like for the brightness asymmetry, a tilt angle asymmetry exists between the two arms that becomes increasingly extreme at large separations. The outer tilt angle of 7.2 deg can only be explained if the outer disk is farther from an edge-on inclination than the inner disk, or if its dust has a stronger scattering anisotropy, or (most likely) both. The strong asymmetries imply the presence of a highly eccentric kinematic disk component, which may have been caused by a disruptive event thought to have taken place at a closer-in location in the disk.