Rapid progress in electrically controlled plasmonics in solids poses a question about possible 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 the kinetic equation with microscopic boundary conditions at the interfaces, followed by perturbation theory with respect to transport nonlocality. The lifetime of the plasmon in an electronically open ballistic system appears to be finite, of the order of conductor length divided by carrier Fermi velocity. The reflection loss of the plasmon incident on the contact of the semiconductor and perfectly conducting metal also appears to be finite, of the order of Fermi velocity divided by wave phase velocity. Recent experiments on plasmon-assisted photodetection [Nat. Commun. 9, 5392 (2018)NCAOBW2041-172310.1038/s41467-018-07848-w] are discussed in light of the proposed lead-induced damping phenomenon.