The effect of cavity dispersion on the dynamics of bound soliton states in a fiber laser has been studied both experimentally and numerically. The mode-locking mechanism in a laser was provided by the frequency-shifted feedback to avoid the influence of soliton attraction that could be induced by saturable absorption. It was found that phase-locked bound solitons are stable for dispersion below the "threshold" value of 0.2 ps/nm which depends on the other cavity parameters. For higher dispersion the bound states collapse resulting in the multiple weakly-interacting soliton regime, circulating randomly within the cavity.