Reinforcement learning (RL) has become essential for unlocking advanced reasoning capabilities in large language models (LLMs). RL workflows involve interleaving rollout and training stages with fundamentally different resource requirements. Rollout typically dominates overall execution time, yet scales efficiently through multiple independent instances. In contrast, training requires tightly-coupled GPUs with full-mesh communication. Existing RL frameworks fall into two categories: co-located and disaggregated architectures. Co-located frameworks fail to address this resource tension by forcing both stages to share the same GPUs. Disaggregated architectures, without modifications of well-established RL algorithms, suffer from resource under-utilization. Meanwhile, preemptible GPU resources, i.e., spot instances on public clouds and spare capacity in production clusters, present significant cost-saving opportunities for accelerating RL workflows, if efficiently harvested for rollout. In this paper, we present RLBoost, a framework for cost-efficient RL training that harvests preemptible GPU resources. Our key insight is that rollout's stateless and embarrassingly parallel nature aligns perfectly with preemptible and often fragmented resources. To efficiently utilize these resources despite frequent and unpredictable availability changes, RLBoost adopts a hybrid architecture with three key techniques: (1) adaptive rollout offload to dynamically adjust workloads on the reserved (on-demand) cluster, (2) pull-based weight transfer that quickly provisions newly available instances, and (3) token-level response collection and migration for efficient preemption handling and continuous load balancing. Extensive experiments show RLBoost increases training throughput by 1.51x-1.97x while improving cost efficiency by 28%-49% compared to using only on-demand GPU resources.