My understanding is that creditors must file a claim within the prescribing filing period.
However, your brother, if he was the executor or personal representative, did have duty to notify all known creditors that he had opened probate and that they needed to respond with their claims within the prescribed time period. (It's 120 days in CA, but might be different in your state.) When I was handling my late father's estate, I did send specific notices to American Express, his Visa bank and to a pharmacy where he had filled various prescriptions. In the case of the credit card companies, I called their 800 number and verified where to send the letters, copy of the death certificate, etc.
If your brother failed to specifically notify this particular creditor, it is possible that the creditor could petition the probate court to reopen the estate on the grounds that it failed to get notice. (This statement may be true even if he put those notices in a local newspaper.) Whether the doctor's office or the collection agency that has the account would do so is another matter entirely. The smaller the debt is, the less likely it would be that it would pursue this one in that matter.
If the estate truly is closed, I would suggest that your brother write the doctor's office or collection agency a letter stating that the debt is not his, the time limt for filing a creditor's claim with the estate expired and that the probate court has closed the case. He should include a copy of the probate court order. If your brother is dealing with a collection agency, he can insist that all future communications be in writing, pursuant to the Fair Debt Collections Law. However, if it is the original creditor, i.e., the doctor's office, that particular law does not apply to it. In that case, if they continue to call, he can investigate whether state law might give him some protection or he can let an answering machine take his calls and just not return any concerning this matter.