The definition Finish (b) refers to errors in sailing the course made at the line.
The RC may score her NSC when she crosses the line.

The RO must score the boat NSC.  However, the definition of finish allows the boat to correct that error as long as she continues to sail the course.  
See case 148:   https://www.racingrulesofsailing.org/cases/2423?page=15

In which case the RC can correct her score based on their own observations (RRS 90.3(c). Or the boat can request redress in the basis that she was scored NSC improperly.

Our SI's always allow the PRO to grant a trailing boat or boats a "finish in place."
In Johan's instance, if the boat wants to go back and correct her course, the PRO could call her back and score her in last place, which she would have eventually achieved.

Since it is a definition which can't be change, I would caution you to use the word Finish in your instruction.   Better language could be:  
If the race committee determines that the finishing order of some boats in a race is unlikely to change, it may use reasonable discretion to score those boats still racing points equal to their position in the race. This changes RRS A3, A4 and A5.

I think Peter's post above referring to Case 148 could be misunderstood.

Case 148 requires that, for a boat that crosses the finishing line having made a RRS 28 error, to be continuing to sail the course so as to return to the course side and correct her error, her action  must be consistent with continuing to sail the course.

The case provides an example of actions not consistent with continuing to sail the course:

After crossing the finishing line, ... X eased her main sheet, luffed her sail and stopped for 30 seconds. Then she sailed [back to the cours  side to correct her error] and crossed the finishing line from the course side a second time.

Case 148 is interesting.  It was always my belief the "continuing to sail the course" applied to circumstances where the course passed through the finishing line (often a multi-lap race).  A boat passing through finishing line after lap 1 would "continue to sail the race" when they went on an sailed lap 2.  The case opens up a wider meaning and includes cases where the boat passes through the line but "if at all times between her first and second crossing of the line, her actions were consistent with sailing the course, then she meets exception (c) and she finished when she crossed the line for the second time."  I think this is a limited exception.  She can't cross the line, sail in the wrong direction for the course or let out her sails to pause.  

Andrew, 

Another simple example is with a W/L course and the finishing line set to leeward of the leeward mark, a boat overruns the leeward mark, through gear failure, poor boat handling or whatever, passes  through the finishing line then turns upwind to round the mark and sail the next leg.

John re: “Another simple example is with a W/L course and the finishing line set to leeward of the leeward mark, a boat overruns the leeward mark, through gear failure, poor boat handling or whatever, passes  through the finishing line then turns upwind to round the mark and sail the next leg.”

Happened to me a few weekends ago. We were racing in 20g30+ W/L with a gate and the RC/start/finish-line not far to leeward of the gate.  A 30kt gust hit us before our takedown and it took all I had to keep the boat under the sail as I sailed through the gate (luckily), crossed the finish line, finally able to douse and rounded the RC and later the mark. 

Previously the RC was obliged to protest a boat for not sailing the course.
The current rule means that the RC can penalise a boat without a hearing. Any boat that disagrees with this score can:
- put in a scoring enquiry setting out how she did sail the course. The RC can consider this and may change the score
-  request redress, preferably after a rejected scoring enquiry.. 

Gordon

Said Created: Today 12:50

That's not correct.   There was no obligation.

case 128 in 2017 said

As rule 60.2(a) states, the race committee may protest A.

That's not exactly correct either.  This time there is an obligation. 

RRS A5.2 and RRS A5.3 say

A boat that did not start, did not sail the course, did not finish, retired or was disqualified shall be scored points for the finishing place one more than the number of boats entered in the series.

Previously the RC was obliged to protest if they wanted to do something about the breach of rule 28. They always had the option to do nothing

Now, if the RC wants to do something about it they can:
-  decide themselves that the boat did not sail the course and score her NSC
- protest her (if for instance the RC is not 100% certain) and let the PC take evidence and find facts.
The option to do nothing still exists.