Don't try to staple it all the way through the packet.
First, reinforce the torn corner. I usually use post-it notes and tape, which do not last long-term if it gets a lot of use. If you need to use these packets for a while, you might want to use paper tape.
Second, staple the front sheet to the next set of sheets, anywhere from 5 to fifteen pages. Either staple it as close to the original staple as you can, or along a natural fold point if that's not practical. Preferably use more than one staple in more than one position - moving the paper around while attached to as single staple is what caused the problem in the first place. So if the original staple was in the top corner, either place two parallel staples a little farther "in", or two to three staples across the top or along the side. It's not a great long-term solution, but it should last a few weeks if you're careful.
Proactively, when you first get the packet reinforce the first page across the staple with something that flexes well (such as duct tape), and over the crease lines at the edge of the paper. If it's a top corner staple, for example, take a piece of duct tape a little over an inch square and put it over the paper and staple, then wrap the edges over the sides of the paper (you can cut a small bit off the corner of the tape to prevent overlap).