How to call system that only consumes energy/matter, but not give away? How to call system that only consumes energy/matter, but not give away?
I know that there are open and dissipative systems, but they can both consume/produce energy/substance.
What about the systems that only consume them?
 A: As we know in physics any macroscopic body at temperature above absolute zero will emit radiation. That is, energy. 
Black holes are probably the best at 'not emitting'. Anything at temperature that is not a BH will emit more. The equivalent temperatures of bigger sized BHs (well, even the smaller ones like stellar sizes but not the microscopic BHs that may not even exist), are way below 1 degree Kelvin. They can emit for billions of years so little you never will see them (though you could detect them through their gravitational forces, or if they collide or suck in lots of nearby matter with some of it also showing as gas jets going out). BHs can absorb matter with no release of any, but if too much matter part of the matter gets spun out before it ever reaches the BH.
For microscopic objects, or really anything with just a few particles where temperature (i.e., statistical mechanics or thermodynamics) makes no sense it depends on what particles they are. For those, dark matter does not emit any electromagnetic radiation, and it may not even interact except through the weak interactions. So it may also not consume much. We've never detected anything from them anyway except their gravitational forces. Unfortunately, we also don't know what they are, yet. 
So if no BHs you can grab, just get the coldest gas you can get, things like liquid helium and other super cold substances. The colder the least output. But if they are in a hotter environment (heat bath), they will absorb and emit till they reach an equilibrium with that heat bath. 
A: Sink (see dictionary definitions bellow).
But "sink" is usually only part of a system. A system that has only a sink of energy/particles, with no source doesn't have a established name AFAIK, but a couple of names that could be quite acceptable are:


*

*purely dissipative system

*exclusively dissipative system

*fully dissipative system

*pure loss system
The kind of system that might refer to is a pendulum: when subject only to gravity, it's conservative; when also to friction, but no forcing, it's purely dissipative; but when it's subject to friction and forcing, it's still a dissipative system, so a qualifier such as "purely" makes it clear the absence of energy sources.

Definition of sink:

2 sink
noun 
5:  a body or process that acts as a storage device or disposal mechanism: such asa :  heat sink; broadly :  a device that collects or dissipates energy (such as radiation)b :  a reactant with or absorber of a substance forests are a sink for carbon dioxide

Source: https://www.merriam-webster.com/dictionary/sink

sink
n.

  
*A natural or artificial means of absorbing or removing a substance or a form of energy from a system.
  

Source: http://www.thefreedictionary.com/sink
