Following the conversation here, I am wondering if anyone knows of an example of dual pair with 4-dimensional N=1 SUSY which relates a non-Abelian gauge theory on one side to a theory with a Lagrangian description but no non-trivial gauge group. Cannot think of one off the top of my head, which doesn't mean it does not exist or even is well-known...
This feels a little trivial, but I don't see why it isn't an example of what you want: Seiberg duality typically relates an $SU(N_c$) gauge theory with $N_f$ flavors to an $SU(N_f - N_c$) gauge theory. There are degenerate cases when $N_f - N_c = 1$ or $0$, which don't correspond to any dynamical gauge group in the infrared. These are usually described in terms of quantum moduli spaces (s-confining when $N_f = N_c + 1$ and chiral symmetry breaking when $N_f = N_c$), with the low energy fields given by mesons and baryons, but you can equally well describe these as the "dual" quarks and mesons of the usual Seiberg duality, in a degenerate limit without gauge fields coupling to them.
Of course, in the same sense, nonsupersymmetric QCD is dual to a theory of massless pions and no gauge symmetry.