Remember this layout I posted awhile back. I am not sure if it's clear from this image but the title is made from fabric.
By running fabric through a Xyron Create-A-Sticker machine loaded with permanent adhesive the fabric is given weight and it not only will hold up to die-cutting but it's also self adhesive ... bonus. Simply cut your favorite fabric to fit the size machine you have. I like to run a Popsicle stick across the fabric to remove any air bubbles before die-cutting. I then cut my title with my Quickutz Studio alpha. I would suggest going for larger images they will hold up better to manhandling. To pull the backing off the alphas I used my paper piercer. Although I have yet to try it I bet you could also run reinforced fabric through a Cuttlebug/Big Shot or any other crank die-cutting tools.
It's ideas like this that make me want to run out and buy a bunch more dies for my Cuttlebug and I need that like a need a hole in my head.