I mentioned before I often cut my recycled materials into stencils. They are chipboard, often fairly thin, and will occasionally be floppy and weak.
It helps tremendously to add acrylic paint to your stencil. Lay the thin, floppy stencil down flat and spread acrylic paint over it. Try not to get the paint beneath the stencil, but you can cut any off with a craft knife if that does happen. The paint is not wiped off, you leave it on the stencil to dry. This will stiffen the stencil and make it much easier to use.
I found a stencil in my stash which is plastic, but incredibly thin and difficult to use. I just did the same thing with that one. You can add several layers of paint to the stencil until it is sturdy enough for your taste.
This also frees up other options for DIY stencils: card stock, manila file folders, junk mail, fun foam, anything and everything can be made into a stencil. (If you have stamps you love-stamp it onto something and cut out the design. Now you have the image as a stencil too.) By covering the stencil with paint, you’re able to make them last a long time for the cost of leftover paint.