http://inrng.com/2014/07/tour-de-france-time-cut-calculation/..the rule includes two exceptions. Here’s the wording:
Finishing times may be adapted under exceptional situations and unforeseen acts of God (weather conditions, blocked roads, serious accident or incident, etc.) according to the assessment of the Stewards’ Committee, with the agreement of the race management. If the percentage of eliminated riders rises above 20% of starters in the stage, permitted finishing times may be increased upon the decision of the Stewards’ Committee, with the agreement of the race management. It is understood that the riders who finish within the new permitted times will qualify for following stages, without a precedent being set for the rest of the race.
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The second point is the safety in numbers element where the gruppetto might
contain 20% of the field. The idea is that
the race cannot afford to see the peloton reduced by a mountain stage. But this is subjective and only applied in rare cases and when it happens riders are docked points from the points competition, a real penalty for any sprinters who miss the time cut as if they’re allowed in the race their chances of taking the green jersey can vanish.