Incidental entanglement in fishing gear is arguably the most serious threat to many populations of small cetaceans, judging by the alarming number of captured animals. However, other aspects of this threat, such as the potential capture of mother-offspring pairs or reproductive pairs, could be equally or even more significant but have rarely been evaluated. Using a combination of demographic and genetic data we provide evidence that i) Franciscana dolphin pairs that are potentially reproductive and mother-offspring pairs form temporal bonds, and ii) are entangled simultaneously. Our results highlight potential demographic and genetic impacts of by-catch to cetacean populations: the joint entanglement of mother-offspring or reproductive pairs, compared to random individuals, might exacerbate the demographic consequences of by-catch, and the loss of groups of relatives means that significant components of genetic diversity could be lost together. Given the social nature of many odontocetes (toothed cetaceans), we suggest that these potential impacts could be rather general to the group and therefore by-catch could be more detrimental than previously considered.