The ionization dynamics of He nanodroplets irradiated with intense femtosecond extreme ultraviolet pulses of up to 10^13 W/cm2 power density have been investigated by photoelectron spectroscopy. Helium droplets were resonantly excited to atomiclike 2p states with a photon energy of 21.4 eV, below the ionization potential (Ip), and directly into the ionization continuum with 42.8 eV photons. While electron emission following direct ionization above Ip is well explained within a model based on a sequence of direct electron emission events, the resonant excitation provides evidence of a new, collective ionization mechanism involving many excited atomiclike 2p states. With increasing power density the direct photoline due to an interatomic Coulombic decay disappears. It indicates that ionization occurs due to energy exchange between at least three excited atoms proceeding on a femtosecond time scale. In agreement with recent theoretical work the novel ionization process is very efficient and it is expected to be important for many other systems.