One of the principal aspects of the dynamic fracture of finite-size one dimensional linear oscillator chains was studied. The study attempted to find an effect that was missed in case of continual analog findings, considering a discrete analog of the elastic rod as represented by a chain of identical oscillators with on fixed ends. The aim was to solve the problem of chain oscillators through a wave equation by the method of finite differences, and carrying out the discretization only with respect to the coordinate. Breakage of some link occurs in one of the subsequent instants in the system performing free oscillations, if the chain was initially in the extended state and the distance between lumped masses was close to a certain critical value. The analysis resolved that the preliminarily extended chain can break upon sudden unloading, and can take place in a chain of arbitrary length chain.