I think you have to seriously consider a scenario in which our missing individual never had the opportunity to signal, write, or attach anything to the dog's collar. Perhaps a fall with no ability to function afterward.
Surely this person would be signaling in some manner if he could do that.
Bummer.
Point taken, however you also have to think that if this person did have the materials to write and attach a message to the dog's collar does not imply he would have other ways/materials to signal with. I can think of many easily plausible injury scenarios where the person would not have the ability to signal even if he had the materials...which we may never know what the person was carrying in terms of a PSK.
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Earth and sky, woods and fields, lakes and rivers, the mountain and the sea, are excellent schoolmasters, and teach some of us more than we can ever learn from books.
John Lubbock