The recent interest in non-Hermitian systems has significantly broadened their application across condensed-matter physics, offering a unique framework to explore out-of-equilibrium phenomena. Simultaneously, altermagnets have emerged as a distinct magnetic class, characterized by unconventional spin-split bands protected by crystal symmetries. In this work, we investigate the interplay between non-Hermitian dynamics and spin transport in these materials, focusing on the Edelstein effect. We demonstrate that the introduction of non-Hermiticity in $d$-wave altermagnets and $p$-wave unconventional magnets opens novel susceptibility components that are inaccessible in Hermitian counterparts. Fundamentally, the dissipation breaks standard momentum selection rules, dynamically converting previously asymmetric channels into even-parity configurations under spatial inversion to allow macroscopic spin accumulation. Crucially, our results show that this nonconservative nature leads to the selective gain and loss of specific spin components, which can be finely tuned by the interplay between dissipation, the magnetic order parameter, and the Néel vector orientation. This phenomenon provides a new route for manipulating spin degrees of freedom through controlled nonconservative processes in emerging unconventional magnetic materials.

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