The mechanism whereby an enveloped virus leaves a host cell is called

Release or egress

Explanation:

Virus can reproduce only within a host cell, this cycle of infection begins with the attachment, where the virus attaches to a specific receptor site on the host cell, after this comes the entry, in the case of enveloped virus, the envelope can fuse directly with the cell membrane to enter the cell, they can also enter through endocytosis. After entering the cell the virus initiates a replication  and assembly mechanism depending on its genome, finally, the last stage of viral replication is the release or egress of the new virions produced in the host organism, some viruses can be released when the host cell dies, but some can leave infected cells by budding through the membrane without directly killing the cell.

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