The objective of this article is to determine as conclusively as possible if the implementation of a UBI (universal basic income) would lead to a significant reduction in the working age population labour supply. If this were true, implementation of a UBI would be unsustainable. To do this, we will compile empirical evidence from studies over the last few decades on the effects of implementation of a UBI on employment. We apply the PRISMA methodology to better judge their validity, which ensures maximum reliability of the results by avoiding biases and making the work reproducible. Given that the methodologies used in these studies are diverse, they are reviewed to contextualize the results taking into account the possible limitations detected in these methodologies. While many authors have been writing about this issue citing experiences or experiments, the added value of this article is that it performs a systematic review following a widely tested scientific methodology. Over 1,200 documents that discuss the UBI/employment relationship have been reviewed. We found a total of 50 empirical cases, of which 18 were selected, and 38 studies with contrasted empirical evidence on this relationship. The results speak for themselves: despite a detailed search, we have not found any evidence of a significant reduction in labour supply; instead we found evidence that labour supply increases globally among adults, men and women, young and old; and the existence of some insignificant and functional reductions to the system such as a decrease in workers from the following categories: children, the elderly, the sick, those with disabilities, women with young children to look after, or young people who continued studying. These reductions do not reduce overall supply because it is largely offset by increased supply from other members of the community.