Quantum scattering of particles by black holes is governed by two different processes. One of them, which is well known, is due to those processes that take place outside the horizon; it is often called the greybody factor. Another one is related to the recently discovered effect of reflection on the horizon. This quantum phenomenon is due to those effects that take place strictly on the horizon. The present work shows that the reflection on the horizon has a very strong qualitative impact on the absorption cross section. The classical work of Unruh (1976) showed that the absorption cross section for low energy particles equals the area of the horizon. However, the reflection on the horizon reduces this cross section, making it zero in the infrared limit (i.e. for very low energies). This effect diminishes ability of black holes to accumulate matter, which may have numerous implications. For example, it may be very important during formation of small primordial black holes. It is argued that the effect has a general bearing, it should manifest itself for different impact particles and different black holes, including the Kerr rotating black holes.