Objective: Survival analysis is central to medical prediction, yet large language models (LLMs) are rarely used as end-to-end survival models because censoring prevents straightforward supervised fine-tuning. Here we present LLMSurvival, a framework that enables censoring-aware survival analysis with unmodified LLMs operating directly on tabular clinical data. Materials and Methods: LLMSurvival reformulates time-to-event prediction as pairwise ranking among comparable subjects, and derives test-time risk by aggregating comparisons against anchor individuals from the training cohort. Results: Across two clinical tasks (ICU mortality prediction in MIMIC-IV and fragility fracture prediction in a NewYork-Presbyterian/Weill Cornell Medicine cohort), LLMSurvival improves overall concordance over Cox proportional hazards modeling by 3.1% for ICU mortality and 0.5% for fracture risk, 2.1% on average for ICU mortality and 2.8% for fracture risk over three established deep learning survival models. Discussion: The results show that survival modeling with censoring can be made compatible with LLM fine-tuning through comparison-based reformulation. The framework demonstrates high portability and superior performance over expert curated scores like SAPS-II and FRAX scores across diverse clinical context. Furthermore, the framework supports local deployment, as compact, publicly available base models provide sufficient performance. Conclusion: The LLMSurvival framework serves as a proof of concept for an integrated, censoring-conscious approach to survival analysis via LLMs.