  Representations of the (Lorentz) conformal group with the soft operators as
highest weight vectors have two universal properties, which we clearly state in
this paper. Given a soft operator with a certain dimension and spin, the first
property is about the existence of "(large) gauge transformation" that acts on
the soft operator. The second property is the decoupling of (large)
gauge-invariant null-states of the soft operators from the $S$-matrix elements.
In each case, the decoupling equation has the form of zero field-strength
condition with the soft operator as the (gauge) potential. Null-state
decoupling effectively reduces the number of polarisation states of the soft
particle and is crucial in deriving soft-theorems from the Ward identities of
asymptotic symmetries. To the best of our understanding, these properties are
not directly related to the Lorentz invariance of the $S$-matrix or the
existence of asymptotic symmetries. We also verify that the results obtained
from the decoupling of null-states are consistent with the leading and
subleading soft-theorems with finite energy massive and massless particles in
the external legs.
