In some conversations involving persons with Alzheimers disease, the participants may have to deal with the difficulty that they do not share a common ground in terms of not only who is alive or dead, but even more, who could possibly be alive. It is as if the participants face a reality disjunction. There are very few empirical studies of this difficulty in conversations involving persons with Alzheimers disease or other kinds of dementia diagnoses. Often studies of confabulation have a focus on the behavior and experience of the healthy participants, but rarely on the interaction and the collaborative contributions made by the person with dementia. In the present article, we discuss various strategies used by all participants in an everyday conversation. The material consists of an hour long everyday conversation between a woman with Alzheimers disease and two healthy participants (relatives). This conversation is analyzed by looking at the organization of the interaction with an emphasis on how the participants deal with instances of reality disjunctions. The result from the analysis demonstrates that both the healthy participants as well as the person with dementia together skillfully avoid the face threats posed by reality disjunctive contributions by not pursuing argumentative lines that in the end might jeopardize both the collaborative and the personal relations.