Protein quality control (PQC) systems are crucial for maintaining cellular proteostasis, particularly under stress that promotes misfolded protein accumulation. A central component of this response is the assembly of stress granules (SGs), cytoplasmic condensates of RNA and proteins that temporarily stall translation. Aberrant SG dynamics, often linked to mutations in SG proteins, contribute to neurodegenerative diseases such as amyotrophic lateral sclerosis (ALS), where persistent protein aggregates are hallmarks. This review examines the emerging role of the ubiquitin-like modifier NEDD8 and its deconjugating enzyme NEDP1 in regulating SG homeostasis. Recent studies identify NEDP1 as a critical factor controlling SG clearance. Inhibition of NEDP1 enhances SG turnover, prevents pathological solidification, and promotes the disassembly of toxic aggregates through hyper-NEDDylation of PARP1, a DNA repair enzyme that also governs SG dynamics. Unlike broad-spectrum PARP1 inhibitors, which can impair DNA repair and cause cytotoxicity, NEDP1 inhibition offers a stress-specific approach that preserves normal cellular functions. Encouragingly, NEDP1 inhibition effectively causes aggregate elimination in ALS patient-derived fibroblasts and restores motility in Caenorhabditis elegans disease models. Altogether, these findings highlight NEDP1 as a key regulator of SG regulation and a promising therapeutic target for ALS and related neurodegenerative disorders.