Short answer to your question is they don't follow up / notify the FFL. You typically wait three days to complete the transaction. That does not mean the FFL has to complete the transaction, such as in the case of
Mark Kelly.
Your state may have a longer waiting period than three days. I would contact my FFL for course of action.
~Whitney
https://www.law.cornell.edu/cfr/text/28/25.6
§ 25.6 Accessing records in the system. (a) FFLs may initiate a NICS background check only in connection with a proposed firearm transfer as required by the Brady Act. FFLs are strictly prohibited from initiating a NICS background check for any other purpose. The process of accessing the NICS for the purpose of conducting a NICS background check is initiated by an FFL's contacting the FBI NICS Operations Center (by telephone or electronic dial-up access) or a POC. FFLs in each state will be advised by the ATF whether they are required to initiate NICS background checks with the NICS Operations Center or a POC and how they are to do so.
(b)
Access to the NICS through the FBI NICS Operations Center. FFLs may contact the NICS Operations Center by use of a toll-free telephone number, only during its regular business hours. In addition to telephone access, toll-free electronic dial-up access to the NICS will be provided to FFLs after the beginning of the NICS operation. FFLs with electronic dial-up access will be able to contact the NICS 24 hours each day, excluding scheduled and unscheduled downtime.
(c)
(1)
The FBI NICS Operations Center, upon receiving an FFL telephone or electronic dial-up request for a background check, will:
(i)
Verify the FFL Number and code word;
(ii) Assign a NICS Transaction Number (NTN) to a valid inquiry and provide the NTN to the FFL;
(iii) Search the relevant databases (i.e., NICS Index, NCIC, III) for any matching records; and
(iv) Provide the following NICS responses based upon the consolidated NICS search results to the FFL that requested the background check:
(A) “Proceed” response, if no disqualifying information was found in the NICS Index, NCIC, or III.
(B)
“Delayed” response, if the NICS search finds a record that requires more research to determine whether the prospective transferee is disqualified from possessing a firearm by Federal or state law.
A “Delayed” response to the FFL indicates that the firearm transfer should not proceed pending receipt of a follow-up “Proceed” response from the NICS or the expiration of three business days (exclusive of the day on which the query is made), whichever occurs first. (Example: An FFL requests a NICS check on a prospective firearm transferee at 9:00 a.m. on Friday and shortly thereafter receives a “Delayed” response from the NICS. If state offices in the state in which the FFL is located are closed on Saturday and Sunday and open the following Monday, Tuesday, and Wednesday, and the NICS has not yet responded with a “Proceed” or “Denied” response, the FFL may transfer the firearm at 12:01 a.m. Thursday.)
(C) “Denied” response, when at least one matching record is found in either the NICS Index, NCIC, or III that provides information demonstrating that receipt of a firearm by the prospective transferee would violate
18 U.S.C. 922 or state law. The “Denied” response will be provided to the requesting FFL by the NICS Operations Center during its regular business hours.
(emphasis mine)
https://www.law.cornell.edu/cfr/text/28/25.2 Link to section of CFR that provides definitions.
Delayed means the response given to the FFL indicating that the transaction is in an “Open” status and that more research is required prior to a NICS “Proceed” or “Denied” response. A “Delayed” response to the FFL indicates that it would be unlawful to transfer the firearm until receipt of a follow-up “Proceed” response from the NICS or the expiration of three business days, whichever occurs first.