Stubborn troops benefit from the superior Leadership of the army's General or a character that joined their unit for all Leadership-based tests, but in a Break test they always use their own unmodified Leadership if it's higher than the character's Leadership reduced by the Break test modifiers.
For example, a Stubborn unit has a Ld of 8 and is joined by (or within range of) the army's General, who has a Ld of 10. They can use the General's Ld 10 for Panic tests, Terror tests, etc. If they lose a combat by one point, they are still better off using the General's Ld - that would be modified to 9 by the Break test modifier - but if they had lost the fight by three or more points, they would use their Stubborn Ld 8 instead.
The same would be true of any non-Stubborn character joining a Stubborn unit.
If a character that is Stubborn himself joins a unit, then the unit can use the character's unmodified Leadership for Break tests (effectively becoming Stubborn themselves if they are not already) as well as other Leadership tests.