Corydoras can be subject to rotting of the barbels around their mouths. But it may not affect all of the fish at the same time. Normally this can occur when they are kept in a tank with a dirty substrate or nitrate levels that are too high.
This can cause an infection in their mouths that literally rot away their barbels. You probably need to treat them with something like Maracyn or Maracyn II to combat the infection.
Check your water quality. You may need to vacuum the substrate again and do a pwc if the nitrates are too high. You need to monitor water quality closely until they are healed. You need to fix the root problem to keep this from happening again. If you do, their barbels should grow back.
If your water quality is fine then the only other thing I can think of is that they got damaged somehow, then became infected. Rough substrate could do this. You will probably still need to treat with Maracyn in any case
