answering machines as devices for not being reached — "which has worn so thin that…"
which has worn so thin that very few of Pemulis's friends or customers can abide waiting through the tired thing to leave a message, which Pemulis finds congenial, since no really relevant caller would be fool enough to leave his name on any machine of Pemulis's anyway.
Context
The one piece of communication technology in the brothers' room is engineered, on both ends, to hold contact at bay. Hal's honesty-week outgoing message accidentally tells the exact truth about where he's headed — a disembodied voice whose body "is not now able" — the coming voicelessness announced as a joke. And Pemulis's infinitely recursive machine is a deliberate filter: worn so thin no real caller will wait through it, which is precisely what he wants, since the whole design is to make sure no one who matters ever actually gets through.