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.
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