When the clay is bone dry, at the green stage, a little more pressure on the piece can easily break it. This kind of 'accidents' can be fixed!
Wet the two broken parts with your paint brush on the broken edges and add some clay with your syringe or some thick paste with a paint brush or clay shaper. Attach the two pieces and try to remove any excess clay. Leave it to dry. Sand carefully the seam. If it needs more repairing, add some more clay on the seam and sand again.
Sometimes, although you may try your best, it may be impossible to make the damage 100% invisible. In such case you have two options:
Change your design, covering the broken part with some rough texture or with some additional decoration.
The second choice is more drastic but more painful; I know that, first hand! If you cannot stand anything but perfection, you will have to recycle your clay and start all over again, hoping that this time you will be more careful!
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