Most likely what the player is thinking of is the rule that
The creature retains its hit points
(Alternate Form description)
which is best known to most players because
Wild Shape (Su)
[…] This ability functions like the alternate form special ability
(Wild Shape description)
If the bear warrior’s bear form worked like wild shape, that is, used the alternate form rules, the player would be correct: they wouldn’t have gained any hp from the extra Constitution that the bear form offers, and they wouldn’t lose any hp when that Constitution went away.
However,
A bear warrior can transform into a bear (similar to the polymorph spell) […] his current hit points increase due to his new Constitution, as normal for a rage ability.
(Bear Form description, Complete Warrior pg. 16)
And then, as normal for temporary bonuses to Constitution that expire,
If a character’s Constitution score drops, then he loses 1 hit point per Hit Die for every point by which his Constitution modifier drops.
(Ability Score Loss description)
So the bear warrior’s current hit points decrease due to their Constitution going back to normal when it ends. The bear warrior would, under the rules, lose 120 hp and die. However, the 120 hp that is lost is the same 120 hp that would have been gained when the character first became a bear. If the player was mistakenly applying the wild shape/alternate form rule consistently, they may never have gained the 120 hp in the first place—meaning they should be at 150 hp, not 30 hp, and therefore would not die upon losing 120 hp.
Even if they did gain the 120 hp, and the 30 hp figure is correct and the character should die upon losing bear form, it’s worth noting that the very next sentence about Constitution loss is
A hit point score can’t be reduced by Constitution damage or drain to less than 1 hit point per Hit Die.
A Constitution bonus expiring is not the same thing as Constitution damage or drain; this rule does not apply in this situation, and I’m pretty sure that was intentional—I seem to recall developer commentary confirming that barbarians dying from their rage ending was an intended part of the game. Still, this line exists for a very similar situation, and maybe barbarians dying from their rage ending isn’t really good for your game—it isn’t for mine, and I houserule this situation. You may want to also.
Even if you do not want to houserule this in general, it seems a good practice to avoid making this a “gotcha” for the player—presuming they were sincere in their belief that they would not die from this, that may have affected their decisions leading up to this situation. So letting them survive it at least this one time seems warranted.