We have studied the stability of domains and domain walls in multiferroic BiFeO3 thin films using a combination of piezoelectric force microscopy and phase-field simulations. We have discovered that a film-substrate misfit strain may result in a drastically different thermodynamic stability of two parallel domain walls with the same orientation. A fundamental understanding of the underlying physics, the stress distribution in a domain structure, leads to a novel approach to control the ferroelastic domain stability in the multiferroic BiFeO3 system.