Ultrahigh-intensity laser-plasma physics provides unique light and particle beams as well as novel physical phenomena. A recently available regime is based on the interaction between a relativistic intensity few-cycle laser pulse and a sub-wavelength-sized mass-limited plasma target. Here, we investigate the generation of electron bunches under these extreme conditions by means of particle-in-cell simulations. In a first step, up to all electrons are expelled from the nanodroplet and gain relativistic energy from time-dependent local field enhancement at the surface. After this ejection, the electrons are further accelerated as they copropagate with the laser pulse. As a result, a few, or under specific conditions isolated, pC-class relativistic attosecond electron bunches are generated with laser pulse parameters feasible at state-of-the-art laser facilities. This is particularly interesting for some applications, such as generation of attosecond x-ray pulses via Thomson backscattering.