Systems and methods for fastening tissue include a hollow element and an elongate insertion element. The insertion element has a delivery device including a cone, suture, and needle at a delivery end, and an anchor at an opposite end. The hollow element includes an engagement structure in its interior surface that permits movement of the insertion element through the hollow element in a first direction, and prevents movement of the insertion element through the hollow element in a second direction opposite the first direction. The engagement structure may include a braid or mesh that operates on a finger-trap principle. The hollow element may include an elongate element with a cone, suture, and needle at a delivery end, and an anchor at an opposite end. Alternatively, the hollow element may include a button that incorporates the braid or mesh.
