I have many years of experience in piano rebuilding. Technically the answer is yes. Piano strings can and do break. However, you probably don't have to worry about injury to yourself for two reasons. Typically a piano string will break while it is being manipulated by a piano tuner as a result of corrosion and age and friction at a corroded spot on the string. Seldom will a piano string break while it is being played or just sitting there. Also the piano string is more likely to break near the tuning pins or agraffe. So when it does break the string flys away from you towards the back of the piano. When rebuilding I have had different strings break at different places and on the rare occurence when the string does break away from you and the string flys towards you it tends to stay low and will hit you just a few inches above pin block (on a grand piano)they don't seem to go much further than the lin block area. If you happen to have your hand in that area the string can penetrate your skin and lodge in your finger bone. But it pulls out pretty easily. You have nothing to worry about - - as a player anyway.
14th June, 2017