That depends on the gauge of the cable and how tight it is pulled. In general, cables can bend a fair amount without breaking, as long as they are not pulled too tight. For example, a 26-gauge cable can be bent into a complete circle before breaking, while a 16-gauge cable can only bend into a half-circle.
Ribbon cables are designed to be more flexible than regular cables, so they can bend more easily without breaking. However, if they are too tightly pulled, they can still break or snap.