If there were true, any Christian who commits a sin becomes forever excluded from salvation.
Meditate on that a bit. If this passage is saying what you say it means, that's it. One sin which you choose to commit, and you are done with God. All that remains is for Him to cast you into the lake of fire.
Or it means that there remains no sacrifice for sin that you can still offer. That system is over. Those sacrifices didn't remove sin. They can only remind you that sins remain. But that's been ended.
Jesus' sacrifice for sin put an end to all the others. His offering - Here's an important part to notice - His offering, which has already been offered, removed sin.
There remains no sacrifice for sin because . . . animal sacrifices were ended, and Jesus' sacrifice has already been completed.
The word there, "remains", refers to what's been left behind, what remains. And there remains no sacrifice which you might offer for sin.
Jesus sacrifice put an end to any other sacrifice, so there's nothing left.
However . . . Jesus' sacrifice, well, in the words of Scripture,
10) By the which will we are sanctified through the offering of the body of Jesus Christ once for all.
Hebrews 7:27 - Who needeth not daily, as those high priests, to offer up sacrifice, first for his own sins, and then for the people's: for this he did once, when he offered up himself.
Hebrews 9:12 - Neither by the blood of goats and calves, but by his own blood he entered in once into the holy place, having obtained eternal redemption for us.
Much love!