The recent COVID-19 pandemic led to uncertainty and severe health and economic concerns. Previous studies indicated that owning a companion animal, such as a dog or a cat, has benefits for good mental health. Interactions with animals may help with depression and anxiety, particularly under stress-prone conditions. Human–animal interactions may even improve peer-to-peer social relationships, as well as enhance feelings of respect, trust, and empathy between people. Interestingly, it has also been shown that stress and poor well-being of dog owners negatively affect the well-being of their companion animals. However, a dramatic increase in dog abandonment could potentially occur due to COVID-19 related health, economic and social stresses, as well as due to the inconclusive reports of companion animals being potential COVID-19 carriers. Such a scenario may lead to high costs and considerable public health risks. Accordingly, we hypothesized that the COVID-19 pandemic, and the related social isolation, might lead to dramatic changes in human–dog bidirectional relationships. Using unique prospective and retrospective datasets, our objectives were to investigate how people perceived and acted during the COVID-19 pandemic social isolation, in regards to dog adoption and abandonment; and to examine the bidirectional relationship between the well-being of dog owners and that of their dogs. Overall, according to our analysis, as the social isolation became more stringent during the pandemic, the interest in dog adoption and the adoption rate increased significantly, while abandonment did not change. Moreover, there was a clear association between an individual’s impaired quality of life and their perceptions of a parallel deterioration in the quality of life of their dogs and reports of new behavioral problems. As humans and dogs are both social animals, these findings suggest potential benefits of the human–dog relationships during the COVID-19 pandemic, in accordance with the One Welfare approach that implies that there is a bidirectional connection between the welfare and health of humans and non-human animals. As our climate continues to change, more disasters including pandemics will likely occur, highlighting the importance of research into crisis-driven changes in human–animal relationships.