Can a reference ‘match’ an evidence profile if these have no loci in common?

Cold case reinvestigations are a common occurrence. Occasionally some of the original work was conducted up to 30 years ago using profiling systems of the early 1990s, which targeted HLA-DQA1, ApoB, D1S80 and D17S5. When contemporary work is carried out, if a suspect is identified they will be profiled in contemporary profiling kits such as GlobalFiler. It would be common to then also attempt to profile the evidence profiles in the same contemporary profiling kit. Imagine a scenario where two evidence samples, E₁ and E₂, had previously produced single-source profiles, but only E₂ had any DNA extract left to re-profile with GlobalFiler. At the old loci E₁ matched E₂, and at the new loci E₂ matched the suspect reference. Of interest to the investigation was whether anything could be said about the suspect being a donor of DNA to E₁ even though the reference of the suspect and the profile from E₁ had no loci in common, by using the information from the profile of E₂. This paper explores that possibility.