Conventional Vision-and-Language Navigation (VLN) benchmarks assume instructions are feasible and the referenced target exists, leaving agents ill-equipped to handle false-premise goals. We introduce VLN-NF, a benchmark with false-premise instructions where the target is absent from the specified room and agents must navigate, gather evidence through in-room exploration, and explicitly output NOT-FOUND. VLN-NF is constructed via a scalable pipeline that rewrites VLN instructions using an LLM and verifies target absence with a VLM, producing plausible yet factually incorrect goals. We further propose REV-SPL to jointly evaluate room reaching, exploration coverage, and decision correctness. To address this challenge, we present ROAM, a two-stage hybrid that combines supervised room-level navigation with LLM/VLM-driven in-room exploration guided by a free-space clearance prior. ROAM achieves the best REV-SPL among compared methods, while baselines often under-explore and terminate prematurely under unreliable instructions. VLN-NF project page can be found at https://vln-nf.github.io/.