Achromatic breaks in afterglow light curves of gamma-ray bursts (GRBs) arise naturally when the product of the jet's Lorentz factor \gamma and opening angle \Theta_j satisfies \gamma\Theta_j >> 1. Magnetohydrodynamic (MHD) simulations of collimated GRB jets generally give \gamma\Theta_j <~ 1, suggesting that MHD models are incapable of explaining jet breaks. We work within the collapsar paradigm and use axisymmetric relativistic MHD simulations to explore the effect of a finite stellar envelope on the structure of the jet. Our idealized models treat the jet-stellar envelope interface as a collimating rigid wall, which opens up outside the star to mimic loss of collimation. We find that the onset of deconfinement outside the star causes a burst of acceleration with negligible change in the opening angle. In our fiducial model with a stellar radius equal to 10^4.5 times that of the central compact object, the jet achieves an asymptotic Lorentz factor \gamma ~ 500 far outside the star and an asymptotic opening angle \Theta_j ~ 0.04 rad ~ 2 deg, giving \gamma\Theta_j ~ 20. These values are consistent with observations of typical long-duration GRBs, and explain the occurrence of jet breaks.