On my MacBook Pro running macOS 10.12.3, I can reproduce this by plugging or unplugging a USB speaker during playback; both directions produce similar results:
* audio stops on the old device
* on the new device, a humming noise may be emitted
* audioprocessing events are no longer delivered
When switching back to the original output device, audioprocessing events continue being delivered, and audio continues as expected.
Simplified test case: https://brionv.com/misc/audio.html
Same results with Safari 10 release version, Technical Preview, and WebKit Nightly.
This sounds suspiciously like a bug we fixed in iOS last year; I must have done it in a platform specific area of the Web Audio code. Should be relatively easy to port over.