Update: Google has confirmed to us that "the Limited Edition White Nexus 8GB and 16GB are sold out on Google Play." A sold out limited edition would mean the limited run is over, so the White Nexus 4 is no more on the US Play Store.
Head over to the Play Store listing for a black Nexus 4 and you'll see that in the "Choose another Nexus 4" area below the main splash, its white brethren are nowhere to be found. That's because now, after the 8GB white model was listed no longer for sale, the 16GB edition has suffered the same fate (see page here).
While the URLs for both the 8GB and 16GB white N4s are still functioning, this is likely just to prevent 404s. The devices cannot be discovered directly on the Play Store (though some of you may still seem them - this is just caching). Typically, when Google lists a device "no longer available for sale," this means that the entire stock has been depleted, and that no new stock will be arriving. We've reached out to Google to confirm the news, but you can rest fairly well-assured that this is the end for the white Nexus 4.