Short answer: No (and maybe…).
The long answer is bit more complicated.
Basically, if the debt was incurred (happened) before you filed the bankruptcy, then you can add it to your open case. If the debt was incurred after you filed, then you cannot. (but see below).
When you file a bankruptcy case (7 or 13), you list all of your debts for things that happened up to the moment of filing. So if you are in a car accident as you drive to your attorney’s office to file the paperwork and get rushed to the hospital, you can add those bills, because they happened before you filed the bk.
However, if you have a follow-up with the doctor after you file bk, that follow-up appointment is not covered. It happened after the bk was filed.
On the other hand, let’s say you file bankruptcy, and then receive some collection bills from creditors for things that happened before the bk was filed. You can add those to your current case.
Even more complicated: you visit the doctor before filing, but he forgets to bill you until after we file. This IS covered, because the actual visit/service occurred before the bankruptcy was filed.
It all depends on when the debt was incurred.
With my clients, we try to list every creditor we can. Then we file the case. After filing, I tell them to make a stack of any collection notices they receive after we file. About 2 months after filing, we compare this stack to the list of creditors in the case. If there is someone we forgot, we add them.
Exception for new debt: That being said, if you are in a chapter 13 and incur new debt (like a huge hospital bill), you can convert your case to a chapter 7 and add the new debt. However, this is complicated enough that it deserves its own post.