Let us be clear on the framewoks, in the classical physics framework,as long as we are on the present cosmos, i.e.on earth, there is no absolute zero in velocity. A particle can have a zero velocity in a specific frame, for example in the frame of an elevator moving with constant velocity, but for somebody on the stairs it will be moving with the velocity of the elevator.
Maybe your "absolute zero" refers to temperature which in classical thermodynamics is an attainable goal. It is connected with the average kinetic energy of an ensemble of particles, and if all particles have a velocity=0 then one has a zero in temperature, absolute zero. But it refers to an ensemble of particles, not to one particle. Such an ensemble, even if in a moving elevator will have a temperature zero, because the motion of the system does not affect the temperature definition.
Note that I keep insisting on classical mechanics and thermodynamics. When particles are considered in the underlying quantum framework ( from which classical emerges) there are uncertainties introduced by quantization that do not allow absolute zero temperatures, but that is a long story.