In this work, we study the much less characterized situation of a solid which is deformed at very small strains, with a macroscopic behavior that appears to be perfectly elastic and reversible. In fact, even under such conditions, the system undergoes dissipĆ¢tive stress drops which give rise to dissipation, sometimes called "internal friction". We show that the corresponding stress drops also obeys scale free statistics, however with a power law exponent that is different from the one observed in stationnary flow. This exponent reflects th ecomplex geometry of phase space in the vicinity of a local energy minimum. The statistical analysis also reveals that rapidly quenched amorphous solids are typically marginally stable, i.e. that the equilibrium state can be disturbed, in the thermodynamic limit, by infinitesimal perturbations.