A strawberry runner can develop a new rooted plant while still connected to its parent. Gardeners use this ability, and several related methods, to multiply plants without buying another full-sized specimen.
This is vegetative propagation: producing a plant from existing roots, stems, leaves or buds rather than from seed. Division separates parts that already have useful structures; a cutting must develop missing ones.
The ability depends on the plant, the material and its conditions. It does not mean that any detached piece can become a plant. Propagation takes space, materials and aftercare, and an extra plant is not a guarantee against losing a favourite.