The virus reproduces using the host cells. Two things ultimately take place.
(1) Host cell ends up manufacturing the protein components of the virus as well as the nucleic acid/s of the virus because the latter hijacks the reproductive machinery of the cell and commandeers it for its own ends.
(2) The host cell may either die or survive.
Death of the cell as a direct result of infection by the virus is dependent on the type of virus. Non-enveloped viruses, after replication, usually leave the host cell rupturing the cell membrane resulting in death of the cell.
On the other hand, enveloped viruses leave the cell after replication by budding through the outer membrane of the host cell. Budding frequently does not damage the host cell and in some instances the cell survives while producing large numbers of budding virus particles.
