A number of digital platforms and services have recently emerged that allow users to create posthumous forms of communication, effectively arranging for the delivery of messages from 'beyond the grave'. Despite some evidence of interest and popularity of these services, little is known about how posthumous messages may impact the people who receive them. We present a qualitative study that explores the type of experiences potentially triggered upon receiving such messages. Our findings firstly suggest that posthumous messaging services have the potential to alter the relationship between the bereaved and the deceased, and secondly provide insight into how users make sense of this altered relationship. Through the inference of a set of design considerations for posthumous communication services, we reveal a number of conflicts that are not easily solvable through technological means alone, and which may serve as starting points for further research. Our work extends the growing body of research that is concerned with digital interactions related to death and dying.