A friend of mine is wondering if there is any place in the bible where forgiveness of sin is not connected to salvation. She thinks someone can be forgiven of sin, yet not be saved, as in Matthew 9:2.

I think you may be talking with someone who isn't a clear thinker, or at least not in this case. Salvation is forgiveness of sins. She's kicking against a basic definition. It would be like imagining she can have a husband without being married.

The passage reads, "... Some people brought to him a paralytic, lying on a bed. And when Jesus saw their faith, he said to the paralytic, 'Take heart, my son; your sins are forgiven'" (Matthew 9:2). Forgiveness is relational; this is the biblical view. When Jesus forgave his sins he was forgiven / saved.

If her point is that the word "saved" doesn't appear in the passage--so what? There are multiple ways to express salvation: forgiveness, redemption, justification, ransom, etc. As she begins to read the Bible she will open her mind to the multiple ways the Lord depicts salvation.  Divine forgiveness is always connected to salvation because forgiveness is salvation.