All viruses depend on their host programs. If a host program runs, the virus will run too.  

How can you successfully remove a virus from a computer?

Removing all programs hosting the virusRemoving some of the programs hosting the virus

Yes! Leaving any virus code on a computer will mean the virus will replicate itself again if any of the remaining host programs are run.

Removing only some of the host programs would mean the virus could replicate itself if you run one of the remaining host programs.