The safety alignment of Language Models (LMs) is a critical concern, yet their integrity can be challenged by direct parameter manipulation attacks, such as those potentially induced by fault injection. As LMs are increasingly deployed using low-precision quantization for efficiency, this paper investigates the efficacy of such attacks for jailbreaking aligned LMs across different quantization schemes. We propose gradient-guided attacks, including a tailored progressive bit-level search algorithm introduced herein and a comparative word-level (single weight update) attack. Our evaluation on Llama-3.2-3B, Phi-4-mini, and Llama-3-8B across FP16 (baseline), and weight-only quantization (FP8, INT8, INT4) reveals that quantization significantly influences attack success. While attacks readily achieve high success (>80% Attack Success Rate, ASR) on FP16 models, within an attack budget of 25 perturbations, FP8 and INT8 models exhibit ASRs below 20% and 50%, respectively. Increasing the perturbation budget up to 150 bit-flips, FP8 models maintained ASR below 65%, demonstrating some resilience compared to INT8 and INT4 models that have high ASR. In addition, analysis of perturbation locations revealed differing architectural targets across quantization schemes, with (FP16, INT4) and (INT8, FP8) showing similar characteristics. Besides, jailbreaks induced in FP16 models were highly transferable to subsequent FP8/INT8 quantization (<5% ASR difference), though INT4 significantly reduced transferred ASR (avg. 35% drop). These findings highlight that while common quantization schemes, particularly FP8, increase the difficulty of direct parameter manipulation jailbreaks, vulnerabilities can still persist, especially through post-attack quantization.