  In this letter, we discuss a generalization of the Adler zero to loop
integrands in the planar limit of the $SU(N)$ non-linear sigma model (NLSM).
While possible to maintain at one-loop, the Adler zero for integrands is
violated starting at the two-loop order and is only recovered after
integration. Here we propose a non-zero soft theorem satisfied by loop
integrands with any number of loops and legs. This requires a generalization of
NLSM integrands to an off-shell framework with certain deformed kinematics.
Defining an `algebraic soft limit', we identify a particularly simple
non-vanishing soft behavior of integrands, which we call the `algebraic soft
theorem'. We find that the proposed soft theorem is satisfied by the `surface'
integrand of Arkani-Hamed, Cao, Dong, Figueiredo and He, which is obtained from
the shifted ${\rm Tr}\phi^3$ surfacehedron integrand. Finally, we derive an
on-shell version of the algebraic soft theorem that takes an interesting form
in terms of propagator renormalization factors and lower-loop integrands in a
mixed theory of pions and scalars.
