SRD wrote:
Damage Reduction (Ex)
At 7th level, a barbarian gains damage reduction. Subtract 1 from the damage the barbarian takes each time she is dealt damage from a weapon or a natural attack.
SRD wrote:
Invulnerability (Ex)
At 2nd level, the invulnerable rager gains DR/— equal to half her barbarian level. This damage reduction is doubled against nonlethal damage.
This ability replaces uncanny dodge, improved uncanny dodge, and damage reduction.
SRD wrote:
Damage Reduction
Some magic creatures have the supernatural ability to instantly heal damage from weapons or ignore blows altogether as though they were invulnerable.
The numerical part of a creature's damage reduction (or DR) is the amount of damage the creature ignores from normal attacks. Usually, a certain type of weapon can overcome this reduction (see Overcoming DR). This information is separated from the damage reduction number by a slash. For example, DR 5/magic means that a creature takes 5 less points of damage from all weapons that are not magic. If a dash follows the slash, then the damage reduction is effective against any attack that does not ignore damage reduction.
SRD wrote:
Guarded Life (Ex)
Benefit: While raging, if the barbarian is reduced below 0 hit points, 1 hit point of lethal damage per barbarian level is converted to nonlethal damage. If the barbarian is at negative hit points due to lethal damage, she immediately stabilizes.
So if I understand the argument, the claim is that the converted damage is subject to damage reduction of the invulnerable rager. This rager takes damage and ignores the appropriate amount from the normal DR/-.
Now after this, if the rager is then still reduced below, not at, but below 0 hit points, guarded life then converts an appropriate amount of the remaining lethal damage into nonlethal damage.
So the real question is, what is the source of the nonlethal damage? If the source is guarded life, then it is not a "normal attack" as stated in the damage reduction entry and does not qualify to be ignored.
If however, the nonlethal damage is from the attack, then sure the rager ignores the appropriate amount of nonlethal damage as afforded to him by his invulnerabilty ability. (sounds stupid saying those two words together)
A strict reading might indicate the nonlethal damage is from guarded life, as you wouldn't be dealt nonlethal damage otherwise in this example. I am not saying a agree with this, but simply presenting that as food for thought.