We study the fate of U(1) strings embedded in a non-Abelian gauge theory with the hierarchical pattern of symmetry breaking Gv→U(1) v→ nothing, V≫v. While in the low-energy limit the Abrikosov-Nielsen-Olesen string (flux tube) is perfectly stable, when considered in the full theory it is metastable. We consider the simplest example: the magnetic flux tubes in SU(2) gauge theory with adjoint and fundamental scalars. First, the adjoint scalar develops a vacuum expectation value V breaking SU(2) down to U(1). Then, at a much lower scale, the fundamental scalar (quark) develops a vacuum expectation value v creating the Abrikosov-Nielsen-Olesen string. [We also consider an alternative scenario in which the second breaking, U(1)°→ to an adjoint field.] We suggest an illustrative Ansatz describing an "unwinding" in SU(2) of the winding inherent in the Abrikosov-Nielsen-Olesen strings in U(1). This Ansatz determines an effective 2D theory for the unstable mode on the string world sheet. We calculate the decay rate (per unit length of the string) in this Ansatz and then derive a general formula. The decay rate is exponentially suppressed. The suppressing exponent is proportional to the ratio of the monopole mass squared to the string tension, which is quite natural in view of the string breaking through the monopole-antimonopole pair production. We compare our result with the one given by Schwinger's formula dualized for describing monopole-antimonopole pair production in a magnetic field.