We developed an experimental protocol to analyze the behaviour of a model fiber-based magnetic grabber. A fiber is vertically suspended and fixed to the substrate by its upper end. A magnetic droplet is attached to the free end of the fiber and when a permanent magnet approaches the droplet, the fiber is forced to bow and finally jumps to the magnet. It appears that one can flex the micro-fibers by very small micro or even nano-Newton forces. Using this setup, we discovered a hysteresis of fiber attachment/detachment: the pathway of the fiber jumping to and off the magnet depends on the distance between the magnet and the clamped end. This phenomenon was successfully explained by the Euler-Benoulli model of an elastic beam. The observed hysteresis of fiber attachment/detachment was attributed to the multiple equilibrium configurations of the fiber tip placed in a dipole-type magnetic field.