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Constrained Reinforcement Learning employs trajectory-based cost constraints (such as expected cost, Value at Risk, or Conditional VaR cost) to compute safe policies. The challenge lies in handling these constraints effectively while optimizing expected reward. Existing methods convert such trajectory-based constraints into local cost constraints, but they rely on cost estimates, leading to either aggressive or conservative solutions with regards to cost. We propose an unconstrained formulation that employs reward penalties over states augmented with costs to compute safe policies. Unlike standard primal-dual methods, our approach penalizes only infeasible trajectories through state augmentation. This ensures that increasing the penalty parameter always guarantees a feasible policy, a feature lacking in primal-dual methods. Our approach exhibits strong empirical performance and theoretical properties, offering a fresh paradigm for solving complex Constrained RL problems, including rich constraints like expected cost, Value at Risk, and Conditional Value at Risk. Our experimental results demonstrate superior performance compared to leading approaches across various constraint types on multiple benchmark problems.