There is a fellowship scramble - but I'm not sure how compares to the residency scramble.I would work closely with your residency program director to discuss all the specifics regarding what you need (re: documents). I would have all your ERAS/NRMP IDs, etc handy at the very least.
As FYI:
From NRMP.org:
"What happens if I do not match?
Applicants who learn at noon Eastern Time on Match Day that they did not match to a program can access the List of Unfilled Programs that displays a list of available positions for unmatched applicants. Applicants can also can access the following documents that are posted to the web-based Registration, Ranking, and Results (R3) System at noon eastern time on Match Day:
Match Outcome for All Programs by State, displays the number of positions offered and filled for all programs in the Match.
Match Results Statistics, provides detailed statistical information about the programs, positions, and applicants in the Match."
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And, in case you are interested, program directors are provided this:
"How will I know if my program(s) filled?
Beginning at noon Eastern Time on Match Day, program directors and institutional officials may use their AAMC IDs and password to access the Registration, Ranking, and Results (R3) System and obtain match results and associated reports. Program directors can learn who matched to their program, as well as the number of unfilled positions, if any, by accessing the Confidential Roster of Matched Applicants report. The Confidential Roster of Matched Applicants report can be found under the "My Reports" option on the left bar menu. Institutional officials also may gain access to Match Day reports under the "My Reports" option on the left bar menu.