Recent diffusion-based extreme image compression methods have demonstrated remarkable performance at ultra-low bitrates. However, most approaches require training separate diffusion models for each target bitrate, resulting in substantial computational overhead and hindering practical deployment. Meanwhile, recent studies have shown that joint super-resolution can serve as an effective approach for enhancing low-bitrate reconstruction. However, when moving toward ultra-low bitrate regimes, these methods struggle due to severe information loss, and their reliance on fixed super-resolution scales prevents flexible adaptation across diverse bitrates. To address these limitations, we propose ASSR-EIC, a novel image compression framework that leverages arbitrary-scale super-resolution (ASSR) to support variable-rate extreme image compression (EIC). An arbitrary-scale downsampling module is introduced at the encoder side to provide controllable rate reduction, while a diffusion-based, joint degradation-aware ASSR decoder enables rate-adaptive reconstruction within a single model. We exploit the compression- and rescaling-aware diffusion prior to guide the reconstruction, yielding high fidelity and high realism restoration across diverse compression and rescaling settings. Specifically, we design a global compression-rescaling adaptor that offers holistic guidance for rate adaptation, and a local compression-rescaling modulator that dynamically balances generative and fidelity-oriented behaviors to achieve fine-grained, bitrate-adaptive detail restoration. To further enhance reconstruction quality, we introduce a dual semantic-enhanced design. Extensive experiments demonstrate that ASSR-EIC delivers state-of-the-art performance in extreme image compression while simultaneously supporting flexible bitrate control and adaptive rate-dependent reconstruction.