Archery is a very safe sport if all the normal safety rules are followed be they the club's rules or guidelines issued by equipment manufacturers. All archery equipment manufacturers issue guidelines and warnings for their equipment. Most if not all arrow manufacturers advise you to check all arrows for damage before use. You should check them visually and also flex each arrow.
A small amount of damage can result in arrow failure. This is particularly true for carbon arrows which don't bend, they just break.
Please view the linked video to gain some insight on what can go wrong.