A simple algebraic scheme incorporating the prolate-oblate shape phase transition (SPT) is proposed within the framework of the interacting boson model to describe the quadrupole deformation features of Xe isotopes near $A=130$. The analysis demonstrates that novel $\gamma$-soft modes, characterized by the unusual quadrupole moments $Q\left(2_1^{+}\right)<0$ and $0<Q\left(2_2^{+}\right)\ll \left|Q\left(2_1^{+}\right)\right|$, can emerge near the critical point of this SPT. This finding is further applied to interpret the properties of low-lying states in the relevant Xe nuclei, particularly the experimentally observed nearly vanishing spectroscopic quadrupole moment $Q\left(2_2^{+}\right)$, thereby offering new insights into the structure of a $\gamma$-soft deformed nucleus.

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• Collective levels
• Collective models
• Electromagnetic transitions
• Models based on symmetries
• Nuclear shapes and moments
• Nuclear structure & decays
• 90 ≤ A ≤ 149