By studying the total fusion and breakup cross-sections in the interaction of
 the neutron-halo $^{11}{\rm Be}$ projectile on the lead target $^{208}$Pb,
 it is shown that, even for the neutron-halo projectile, the breakup channel
 remains the most dominant reaction channel at sub-barrier energies, 
 following a characteristic behavior that was also previously verified
 for the case of the proton-halo projectile $^8{\rm B}$. This feature is found to emanate 
 from the enhancement of the breakup cross-section, due to the continuum-continuum 
 couplings coming exclusively from its Coulomb component. 
We further speculate that the 
 enhancement of the Coulomb breakup cross-section at sub-barrier incident energies 
 by the continuum-continuum couplings
 could be associated with the projectile breaking up on the outgoing trajectory, provided 
 these couplings can be proven to delay the breakup process.