Edit - Maybe formulated differently: Does it make sense to talk about the top mass at energies below $m_t$, although in all processes the corresponding energy scale is above $m_t$, because of the rest mass energy of the top quark?
In what sense is it or isn't it meaningful to speak about the top quark mass at energy scales below the top quark mass? Using an effective field theory approach, the top quark decouples at energies below the top quark mass and therefore has no influence on the mass running of the other fermions. Nevertheless, it is possible to compute how the top quark mass $m_t$ changes at energies below $m_t$, for example, because of the energy dependence of the gauge coupling constants. For example, in Updated Estimate of Running Quark Masses the authors compute
We also illustrate the behavior of the heavy quark masses m q ( μ ) ( q = c,b,t ) in Fig. 3. Exactly speaking, the word “the running mass value m Q ( μ )” of a heavy quark Q at a lower energy scale μ than $μ = m_Q ( m_Q )$ loses the meaning. For example, the effective quark flavor number $n_q$ is three at μ = 1 GeV, so that the value of $m_t( μ )$ at $ μ = 1$ GeV has not the meaning. However, for reference, in Fig. 3, we have calculated the value of m Q ( μ ) ( Q = q N ) at μ n ≤ μ < μ n +1 ( n < N ) by using the relation m Q ( μ ) = c m Q R ( N ) ( μ ) [not m Q ( μ ) = c m Q R ( n ) ( μ )].
What do they mean by "loses the meaning"?
Similarly, the authors in Updated Values of Running Quark and Lepton Masses list in table II the top quark mass at various energy scales, for example $m_t(\mu= 2$ GeV) $ \approx 384.4$ GeV, which is considerably different from its value at the $Z$ scale $m_t(\mu= 91$ GeV) $ \approx 171.7$ GeV.