If sterilization inactivates viruses but doesn't necessarily remove them, can residual viral material affect a subsequent culture?

I have a conceptual question about sterilization and contamination.

Suppose a culture medium originally contained a virus and was then properly sterilized. My understanding is that sterilization is intended to eliminate viable/infectious microorganisms, but it doesn't necessarily mean that every physical component or fragment of the virus is removed.

So, how do we distinguish between sterilization and complete removal of viral particles?

More specifically, if residual non-infectious viral particles or viral genetic material remain in the medium, could they ever interfere with or contaminate a subsequently cultured organism or host-cell culture?

I'm mainly asking about the conceptual distinction between sterility, viral inactivation, and complete removal of biological material.