  The fission of a string connecting two charges is an astounding phenomenon in
confining gauge theories. The dynamics of this process have been studied
intensively in recent years, with plenty of numerical results yielding a
dichotomy: the confining string can decay relatively fast or persist up to
extremely long times. Here, we put forward a dynamical localization transition
as the mechanism underlying this dichotomy. To this end, we derive an effective
string breaking description in the light-meson sector of a confined spin chain
and show that the problem can be regarded as a dynamical localization
transition in Fock space. Fast and suppressed string breaking dynamics are
identified with delocalized and localized behavior, respectively. We then
provide a further reduction of the dynamical string breaking problem onto a
quantum impurity model, where the string is represented as an "impurity"
immersed in a meson bath. It is shown that this model features a
localization-delocalization transition, giving a general and simple physical
basis to understand the qualitatively distinct string breaking regimes. These
findings are directly relevant for a wider class of confining lattice models in
any dimension and could be realized on present-day Rydberg quantum simulators.
