  The emergence of quasiparticles is a universal property in integrable
systems. String-type quasiparticles, which are characterized by the string
solutions of Bethe equations, play fundamental roles in the analysis of their
physics. Through an investigation of the Bethe equations in the asymmetric
simple exclusion process, we reveal the existence of string solutions in the
presence of non-Hermiticity resulting from asymmetrical hopping. Because of the
non-Hermiticity, the string solutions exhibit exotic properties such as the
complexification of the center of string solutions and the delocalization of
Bethe quantum numbers. In addition, we find the picture of string-type
quasiparticles collapses in the strong asymmetry regime. The collapse of string
solutions characterizes the transition of eigenstates from bound states to
scattering states.
