I can only speak for the Phoenix market. In Phoenix, there is no shadow inventory. Bank owned/serviced homes are almost all on the market. If they are not, it's because of the time needed to clean them up or some kind of dispute about the mortgage insurance or about some other loan ownership issue. As the market has shot up, defaults are being cured. The default rate is at the lowest point in years. There are homes that should be foreclosed on because the borrowers will never recover, but they are in work out agreements and that will happen as the modifications fail. Anything reasonably priced has multiple offers, the demand is solid. Cash and well qualified conventional buyers are everywhere.
Prices are up sharply, but still well below the peak in most areas. There is price risk because of the artificially low interest rates, but the current crop of buyers are looking at the mortgage payment or are long term investors paying cash. Sellers that can hold on to wait for full recovery are doing so. That reduces inventory as well. It's unlikely these folks will create a deluge as prices go up, but more inventory will balance the market and slow price increases.
Here in Silicon Valley, it's multiple offers everywhere and prices are at or above the last peak in the most desirable areas. Why on earth would anyone keep a foreclosure off the market when they are recovering 100 percent?