Motivation: Read alignment is an important step in RNA-seq analysis as the result of alignment forms the basis for further downstream analysis. However, recent studies have shown that published alignment tools have variable mapping sensitivity and do not necessarily align reads which should have been aligned, a problem we termed as the false-negative non-alignment problem.Results: We have developed Scavenger, a pipeline for recovering unaligned reads using a novel mechanism which utilises information from aligned reads. Scavenger performs recovery of unaligned reads by re-aligning unaligned reads against a putative location derived from aligned reads with sequence similarity against unaligned reads. We show that Scavenger can successfully recover unaligned reads in both simulated and real RNA-seq datasets, including single-cell RNA-seq data. The reads recovered contain more genetic variants compared to previously aligned reads, indicating that divergence between personal and reference genome plays a role in the false-negative non-alignment problem. We also explored the impact of read recovery on downstream analysis, in particular gene expression analysis, and showed that Scavenger is able to both recover genes which were previously non-expressed and also increase gene expression, with lowly expressed genes having the most impact from the addition of recovered reads. We also found that the majority of genes with >1 fold change in expression after recovery are of pseudogenes category, indicating that pseudogenes expression can be substantially affected by the false-negative non-alignment problem.