Cells can repeatedly produce certain proteins. For instance, a silkworm can spin out a thread of silk. That doesn't meant that molecules of silk are alive because they are reproducing.
Any parasite that requires its host for reproduction could be said to be a byproduct of the host continuing its biological functions usually at the expense of the host.
Nature draws no clear lines, humans apply taxonomy, any line we draw about what is alive and what isn't will be arbitrary.
My opinion is a virus is alive as it core process is based on how all life on earth operates through DNA/RNA. That is my arbitrary line, a distinct self contained genetic code that continues to replicate and evolve is alive. If that code can no longer continue replicating successfully it is dead.
To be pedantic, all you need is at most two (or three, maybe?) of the right gender to reproduce in a vacuum (metaphorically) to make it a living organism. A virus can't reproduce with another virus that way because it can't do anything on its own other than float around waiting for a host, no matter how many strains you mix it with. The host does the actual reproducing for the virus.