Usually when a person dies, The Social Security Administration reports their social security number as belonging to the deceased individual. On getting this report of the credit bureaus flag the credit report as belonging to a person who is no longer living.
You also have the option of notifying every creditor and lender that the deceased person has an account with and have them update their records. When this creditor reports the fact that the Count belongs to deceased person the credit bureau will add that information in the credit report. However, reporting a single account as belonging to deceased person is different from flagging the entire credit report. Flagging the entire credit report is a better option as all the lenders will get a notice that the report belongs to deceased person in case anybody tries to steal the information to commit credit fraud. A credit reports that has been flat is not deleted from the credit bureaus immediately. This is done as a security precaution and as a measure to prevent identity theft. If the file work to be deleted immediately and density thief could use the deceased identity to commit credit fraud more easily.
If you find that the records in the credit bureaus have not been updated according to the information issued by the Social Security Administration then you can write to the credit bureau requesting the change and flagging of the credit report. You will probably be asked to send in the required documents in order to identify the individual concerned as deceased.