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Sufficient die depth is essential if you are cutting tall material. Most materials will compress when being cut, but you can only compress so far before you begin to damage your die or material. The average wood backed die with .937 steel rule will have about a 1/4" cavity. However, you have to account for your ejection foam, which limits cavity depth as well.
If you have a 1/4" cavity, you can't cut a 1/4" of paper or plastic because there is no place for the material to go. If you want to cut more material and you have enough pressure to do so, you will need to change your rule height so your product has someplace to go during the cut.