  We show that line defects in a non-Abelian Kitaev spin liquid harbor gapless
one-dimensional Majorana modes if the interaction across the defect falls below
a critical value. Treating the weak interaction at the line defect within a
mean-field approximation, we determine the critical interaction strength as a
function of the external magnetic field. In the gapless regime, we use the
low-energy effective field theory to calculate the spin-lattice relaxation rate
for a nuclear spin near the defect and find a cubic temperature dependence that
agrees with experiments in the Kitaev material $\alpha\text{-RuCl}_3$.
