Although deep reinforcement learning has demonstrated impressive achievements in controlling various autonomous systems, e.g., autonomous vehicles or humanoid robots, its inherent reliance on random exploration raises safety concerns in their real-world applications. To improve system safety during the learning process, a variety of Safe Reinforcement Learning (SRL) algorithms have been proposed, which usually incorporate safety constraints within the Constrained Markov Decision Process (CMDP) framework. However, the efficacy of these SRL algorithms often relies on accurate function approximations, a task that is notably challenging to accomplish in the early learning stages due to data insufficiency. To address this problem, we introduce a Genralizable Safety enhancer (GenSafe) in this work. Leveraging model order reduction techniques, we first construct a Reduced Order Markov Decision Process (ROMDP) as a low-dimensional proxy for the original cost function in CMDP. Then, by solving ROMDP-based constraints that are reformulated from the original cost constraints, the proposed GenSafe refines the actions taken by the agent to enhance the possibility of constraint satisfaction. Essentially, GenSafe acts as an additional safety layer for SRL algorithms, offering broad compatibility across diverse SRL approaches. The performance of GenSafe is examined on multiple SRL benchmark problems. The results show that, it is not only able to improve the safety performance, especially in the early learning phases, but also to maintain the task performance at a satisfactory level.