As the high performance computing (HPC) community continues to push towards exascale computing, HPC applications of today are only affected by soft errors to a small degree but we expect that this will become a more serious issue as HPC systems grow. We propose F-SEFI, a Fine-grained Soft Error Fault Injector, as a tool for profiling software robustness against soft errors. We utilize soft error injection to mimic the impact of errors on logic circuit behavior. Leveraging the open source virtual machine hypervisor QEMU, F-SEFI enables users to modify emulated machine instructions to introduce soft errors. F-SEFI can control what application, which sub-function, when and how to inject soft errors with different granularities, without interference to other applications that share the same environment. We demonstrate use cases of F-SEFI on several benchmark applications with different characteristics to show how data corruption can propagate to incorrect results. The findings from the fault injection campaign can be used for designing robust software and power-efficient hardware.