What Is The Likelihood Of The Mint Reusing

None. The dies are numbered, when retired, they are defaced so they cannot be used again. Some are sold. So just get recycled. The mark you are seeing on your coin, is an incuse mark on the die. Perhaps a die scratch that flattened out in the open fields, by next to a device, thy remain. Inside of a device, they last the longest. If it were part on a hub, then were is the rest of the whole design? It just couldn't happen. So chances are zero.

considering they used the D from the 1914 D cent on the 1916 D dime, and this is proven conclusively, I'm not willing to rule out the mint reusing numbers or mint marks in the die making
processes, somewhere between master hubs, working hubs, master dies and dies.
it's more research than I'm willing to do at this time though to find out where the dates get added or amended each year and how they do it exactly. but the mintmarks are added to working dies back then. I'm not sure where the date gets added in the process. but I have to assume that they carry major design elements for many years without changing the design, until they do change the design or correct it which gets us ODVs and RDVs for any coin series.

it could also be a small die chip and well placed.

I think it's possible.... In 1909, the date was struck into the master die ending the era of repunched and misplaced dates, but I could see the Galvano being made, then a master die, then hub with date added, then working dies and the date being punched in on the master die with mintmarks punched added for working dies and using an identifiable digit, just like the D on the 1916D dime is identifiable as the D on the 1914 D cent.

Just going to say though, in my opinion, I don't think it should be completely ruled out, I think the possibility exists of reusing number punches on the master die, possibly one that is identifiable even from the other 9s which should all be uniform within the year.

HOWEVER I think the minor die chip or scratch is a more likely senario, I have no explanation on why both 9s wouldn't be exactly the same punch used on the master die. or why, if they did use a 4 digit punch on the master die, why they would reuse and modify the 1909 one and not set up a new punch each year all placed nicely.

i'd think a 4 digit punch is likely for uniformity and spacing concerns, Already thinking about this too much. LOL

small die chip or scratch in the die I think.

I know if it were on a master die, likely most every coin would have it as it would move on down to working dies.

I've got to respectfully disagree with you coop, but yes 4 digit did end in 1908.
Wexlers, and other sources, but I'm just going to reference wexlers, "When the Janvier Reduction Lathe was introduced in 1907, the first two digits of the date began to appear on the galvano and thus on the master hubs. This was done so that the master hub could be used to make master dies over a period of several years. Starting with the Lincoln cents in 1909, the last two digits of the date were engraved into the master die for each year."
http://doubleddie.com/58201.html

It wasn't on the master hub, only the first two digits of the date were.
The design with complete date is on the master die on down, but not complete on the master hub in 1909, the first two digits were on the master hub, the last two digits were added on the master dies.

"By the middle of the 1980's the Mint started placing the last two digits of the date on the master design (galvano) and New master hubs were prepared each year for each denomination. At this time the Mint also started placing the mint mark on the master design for all Commemorative and proof coins."

Also Pre-1965 Mintmarks were punched into working dies. After 1965 they were punched into working hubs to reduce the frequency of RPMs.
Starting 1990, the mintmark became part of the master die.
At some point they have since moved the mintmark to the master hub (galvano actually, the master design) for each facility instead of on the master master die. stabilizing the location of the mintmark and eliminating RPMs.
This did require a minimum of 2 master hubs for just P+D of a design, to up to 4 master hubs for P,D,S,and W, technically since 1990 at some point, all elements are now on the master hubs. I believe around 1997 with the switch to single squeeze hubbing, but I can't find a reference to be certain of that year for the mintmarks to be added to the master hub instead of the master dies.

I understand the folly of my original question and agree that it is probably just a coincidental die gouge.

Did they do three-digit dates and just adjust the fourth digit? I've noticed that the last digit is sometimes of a different font/typeset than the others.