The paper investigates non-invertible topological symmetry operators in massive quantum field theories (QFTs) in (1+1) dimensions. The authors show that when this symmetry is spontaneously broken, the particle spectrum often exhibits degeneracies dictated by the non-invertible symmetry. They provide a procedure to determine these allowed multiplets and demonstrate that these degeneracies are robust predictions that do not require integrability or special features of renormalization group (RG) flows. The study is illustrated through examples where the spectrum is known, recovering soliton and particle degeneracies. For instance, the Tricritical Ising model deformed by the subleading Z2 odd operator flows to a gapped phase with two degenerate vacua, which supports a threefold degeneracy of particle states due to the Fibonacci fusion category symmetry. This symmetry implies a degeneracy between solitons and particles, relating the mass of solitons interpolating between vacua and particles supported in a single vacuum. The paper also explores the application of these findings to models where the particle spectrum is known via integrability, such as unitary minimal models deformed by the φ1,3 operator, where the non-invertible symmetry implies a multiplet of 2(n-2) degenerate single-particle states.The paper investigates non-invertible topological symmetry operators in massive quantum field theories (QFTs) in (1+1) dimensions. The authors show that when this symmetry is spontaneously broken, the particle spectrum often exhibits degeneracies dictated by the non-invertible symmetry. They provide a procedure to determine these allowed multiplets and demonstrate that these degeneracies are robust predictions that do not require integrability or special features of renormalization group (RG) flows. The study is illustrated through examples where the spectrum is known, recovering soliton and particle degeneracies. For instance, the Tricritical Ising model deformed by the subleading Z2 odd operator flows to a gapped phase with two degenerate vacua, which supports a threefold degeneracy of particle states due to the Fibonacci fusion category symmetry. This symmetry implies a degeneracy between solitons and particles, relating the mass of solitons interpolating between vacua and particles supported in a single vacuum. The paper also explores the application of these findings to models where the particle spectrum is known via integrability, such as unitary minimal models deformed by the φ1,3 operator, where the non-invertible symmetry implies a multiplet of 2(n-2) degenerate single-particle states.