Knowing that it is extremely unlikely for a capped die strike to escape modern sorting techniques, I was intrigued by an example offered on Ebay of an aluminum token capped die strike, The lot included two pieces that dramatically illustrate the event:

The first image shows the twos pieces as they would have come off the press. The two pieces fit inside one another like a cup and saucer, although it is possible there were one or more intermediate pieces before these two were recovered from the press.
The next image is the obverse or top cup. It has the most dramatic lip, about a quarter of an inch deep. Note that the obverse image is sharp. It should be as it is in direct contact with the die. Basically, a normal token is struck, clear obverse and reverse images. The token has adhered to the top die for whatever reason (it could be the reverse depending on the design of the press--in general there has to be a direction for the metal to go. I am assuming the die comes down, the metal flows up forming the cup feature.). The reverse of the token forms a negative image on the planchet that comes in below it. The press is set for a set thickness, so the extra metal has to go somewhere, i.e. up forming the cup.

Notice the reverse is distorted. Without an original, undistorted example, I don't know how thick the token is supposed to be. Each piece is only one planchet as they weigh the same. When the token stuck to the upper die makes its impression on the new planchet, a reversed, incused image is formed and then the images distort as the metal flows outward to form the upper cup and lower saucer. The lower cup (or saucer) meshes with the upper cup, again the metal flowing up in response to the pressure produced by the descending die. Either the collar is not popping into place or the metal buildup is sufficient to impede its travel.

Notice the negative image inside the lower saucer is distorted as is the positive image on the reverse of the upper cup. The reverse of the cup shows an undistorted image of the token's reverse. It can only be so because the lower die is in normal contact with the lower planchet.
All in all, I thought this was a great example of a mint error that rarely escapes the mint and an interesting addition to my aluminum collection.
Edited 6/14/06 after more thought about how I described some of the process.