Robustness properties of the two-sample Wilcoxon test are established when the assumption of independence between samples is weakened to allow pairing. In particular, the test is shown to be (asymptotically) conservative when the bivariate distribution governing the pairing is positively quadrant dependent.
"Robustness of the Wilcoxon Test to a Certain Dependency Between Samples." Ann. Statist. 2 (1) 177 - 181, January, 1974. https://doi.org/10.1214/aos/1176342623