Like others have stated, the strut boot is actually open on the bottom and is longer than the exposed shaft (in stock config). This helps keep the debri limited to and building on the shaft. For the shocks, the stock shocks are the same way, but when you install better aftermarket shocks, most come with a boot which is fitted to the top and bottom of the exposed shaft. This creates a pocket to hold the debri.
You could cut the bottom of the fitted boot. However, it's not rigid enough.