A turbomachine comprising at least a first rotary assembly with a first shaft, a stator, and bearings secured to the stator and suitable for supporting the shaft, one of the bearings being capable of giving way when an unbalance occurs in the rotary assembly, at least one segment of the shaft being covered in a covering which comprises at least one piece of fabric impregnated with resin and which is for coming into contact with a surrounding portion of the turbomachine when the unbalance occurs in order to protect the first shaft and ensure that there is no risk of the first shaft rupturing. The turbomachine is intended to be used mainly in the field of aviation, and more particularly as an airplane turbojet.