Oh, my goodness, Amanda! That's something that has occurred to me that could happen. Especially with the serger. I think I get close to doing that by trying to push the fabric near the presser foot. Been trying not to do that....
I haven't heard of anything that would protect fingers either, I agree with Adrienne that a seam guide may help. But if your sewing machine has a computer in it for embroidery you might not want to use a magnetic guide. There are others available. If I hear of a finger protecter of sorts, I'll let you know. Good luck!