Gun Jumpers are so fun..

[Maelwys]

The tank grabs and holds the hate, the healer heals the party, the DPS DOes what they do best, if the tnk dies the WHM folows then the DPS tat is usually the case, there are special circumstances that allow the party to continue without a tank but it is difficult without a healer.

Well, there are also specific situations that allow the party to survive without a healer

Tanks can whittle down certain enemies by "Turtling up" when a Healer faceplants (I'm thinking of things like the Demon Wall and certain AK/WP Bosses here) and taking nearly no damage (PLD - mainly Stoneskin spam) or Self-Healing whatever light damage they take (WAR - mainly Inner Beast spam). Bonus points if the party has a Magic-DD (SMN or BLM?) that can throw a Cure or two the Tank's way.

(I even managed that on Aurum Vale once...)

It applies equally for trash mobs, since you can blow your cooldowns and spend time recovering afterwards.
We made it through the entire final floor of AK a few weeks ago with an AFK Healer... they turned up for the start of the last boss fight, then died to AoEs at 50%. We STILL won!