  Context: Surveys in the visible and near-infrared spectral range have
revealed the presence of low-albedo asteroids in cometary like orbits (ACOs).
In contrast to Jupiter family comets (JFCs), ACOs are inactive, but possess
similar orbital parameters. Aims: In this work, we discuss why ACOs are
inactive, whereas JFCs show gas-driven dust activity, although both belong to
the same class of primitive solar system bodies. Methods: We hypothesize that
ACOs and JFCs have formed under the same physical conditions, namely by the
gravitational collapse of ensembles of ice and dust aggregates. We use the
memory effect of dust-aggregate layers under gravitational compression to
discuss under which conditions the gas-driven dust activity of these bodies is
possible. Results: Owing to their smaller sizes, JFCs can sustain gas-driven
dust activity much longer than the bigger ACOs, whose sub-surface regions
possess an increased tensile strength, due to gravitational compression of the
material. The increased tensile strength leads to the passivation against dust
activity after a relatively short time of activity. Conclusions: The
gravitational-collapse model of the formation of planetesimals, together with
the gravitational compression of the sub-surface material simultaneously,
explains the inactivity of ACOs and the gas-driven dust activity of JFCs. Their
initially larger sizes means that ACOs possess a higher tensile strength of
their sub-surface material, which leads to a faster termination of gas-driven
dust activity. Most objects with radii larger than $2 \, \mathrm{km}$ have
already lost their activity due to former gravitational compression of their
current surface material.
