Tim said:
Sin in general has been paid for by the Blood of Christ Jesus.
But the author isn't talking about "sin in general"; he's talking about generic, or unspecified, sin. He doesn't necessarily know his readers personally or what their particular weaknesses or temptations are. He is assuming they have some sinful encumbrances in their lives, and whatever those are, exhorting them to cast them off.
I believe this passage indicates a particular sin - a sin mentioned in Hebrews elsewhere. Unbelief.
He's writing to a church, not unbelievers. While the theme of the book is a warning against the danger of falling away from the faith, he also tells them, "yet in your case, beloved, we feel sure of better things?things that belong to salvation" (Heb. 6:9), and encourages them to persevere in the faith that they already have. When he speaks of Christ as the great High Priest, he says, "We have this as a sure and steadfast anchor of the soul" (6:19); it is their shared experience. It's clear he does not believe they are unbelievers, so it makes no sense for him to be telling them to rid themselves of a sin that in the main they do not possess.