  In non-Hermitian systems, the defective band degeneracies, so-called
exceptional points (EPs), can form robust exceptional lines (ELs) in 3D
momentum space in the absence of any symmetries. Here, we show that a natural
orientation can be assigned to every EL according to the eigenenergy braiding
around it, and prove the source-free principle of ELs as a corollary of the
generalized Fermion doubling theorem for EPs on an arbitrary closed oriented
surface, which indicates that if several ELs flow into a junction, the same
number of outflow ELs from the junction must exist. Based on this principle, we
discover three different mechanisms that can stabilize the junction of ELs and
therefore guarantee the formation of various types of exceptional chains (ECs)
under the protection of mirror, mirror-adjoint, or ${C}_2\mathcal{T}$
symmetries. Furthermore, we analyze the thresholdless perturbations to a
Hermitian nodal line and map out all possible EC configurations that can be
evolved. By strategically designing the structure and materials, we further
exhibit that these exotic ECs can be readily observed in non-Hermitian photonic
crystals. Our results directly manifest the combined effect of spatial symmetry
and topology on the non-Hermitian singularities and pave the way for
manipulating the morphology of ELs in non-Hermitian crystalline systems.
