Using light to manipulate small particles is a powerful tool with numerous practical applications across biophysics and nanotechnology. This experimental technique has achieved significant performance gains by employing shaped wavefronts, most commonly generated with spatial light modulators. Wavefront shaping has also enabled the manipulation of seemingly arbitrary objects beyond the reach of conventional beams. Contrary to this established assumption, we show here the existence of a wide variety of objects resistant to manipulation, even with the optimal wavefront shaping protocol. The counterintuitive shapes of these objects are found using inverse design in two dimensions, providing a foundation for their natural extension to three dimensions. Specifically, we show that the maximal pulling force is reduced by up to four orders of magnitude, and the maximal trapping stiffness is reduced by up to nearly two orders of magnitude. Our findings could prove useful for the development of micromachines that require a predictable mechanical response to arbitrary waves.