She won't. The issue is that blood feathers can't really clot because there isn't a skin layer in the feather shaft to close. So having a broken blood feather is sort of like having a phlebotomy needle hanging out of your vein. Once you pull the feather, her skin can heal. The most important part is that you get the tweezers as close to her skin as possible because you need to get the whole rest of the shaft fragment out. You may see a little bit of bleeding from her skin afterward but corn starch and gentle pressure will stop it.