Current collection by an infinitely long, conducting cylinder in a magnetized plasma, taking into account the magnetic field of the collected current, is discussed. A region of closed magnetic surfaces disconnects the cylinder from infinity. Owing to this, the collected current depends on the ratio between this region and the plasma sheath region and, under some conditions, current reduction arises. It is found that the upper bound limit of current collection is reduced due to this change of magnetic field topology. The effect can be substantial even if the orbit-limited model of current collection is valid. This model is used to find the reduction of the total current collected by a cylinder (e.g., a bare tether). It is shown that this effect strongly depends on plasma density. The results are applied to a tether system in the ionosphere, and it is found that current reduction can be significant for long tethers in typical dayside ionospheric conditions.