Movie or play character without an actor
Solution 1:
I did not find numerous sources online, and what I did find is not very exciting. But it does do the job.
Wikipedia offers the term unseen character (for theatre, comics, film, or television) and the term silent character (for radio and literature).
The same Wikipedia article includes a reference to the term invisible character, as used by F.C. Green in "Some Marginal Notes on Eighteenth-Century French Comedy" (1961).
In all these cases, these terms refer to characters who never appear or speak, but whose existence is necessary for the advancement of the plot.