Rapid progress in electrically-controlled plasmonics in solids poses a question about effects of electronic reservoirs on the properties of plasmons. We find that plasmons in electronically open systems [i.e. in (semi)conductors connected to leads] are prone to an additional damping due to charge carrier penetration into contacts and subsequent thermalization. We develop a theory of such lead-induced damping based on kinetic equation with self-consistent electric field, supplemented by microscopic carrier transport at the interfaces. The lifetime of plasmon in electronically open ballistic system appears to be finite, order of conductor length divided by carrier Fermi (thermal) velocity. The reflection loss of plasmon incident on the contact of semi-conductor and perfectly conducting metal also appears to be finite, order of Fermi velocity divided by wave phase velocity. Recent experiments on plasmon-assisted photodetection are discussed in light of the proposed lead-induced damping phenomenon.