I suspect they sent it back because it's been sent to a collection agency. I don't know how you arrange to make payments once that happens. I don't think the collection agency will take payments but you can ask.
It seems like I had a disputed bill and the collection agency sent it back to the hospital. I paid the hospital the amount we agreed that I actually owed and the hospital canceled the rest. so, it may be possible to arrange to have the bell sent back to the creditor where you can make payments.
I would call the original person to whom you owed the money and ask about it. I doubt very much it's been paid.
However, it is possible that the creditor wrote the bill off. Hospitals can do that under certain circumstances. Again, call the creditor and ask what has happened.
If they wrote it off that info will most likely show up on a credit report.
I hope that you're able to work it out.