Fast HP Regeneration

He's a Gunzerker, and their brawl tree have health regen abilities, being a "tank" class. Especially, from that link:

Level 22-31 – Alternate assigning points into Ain’t Got Time to Bleed (first) and Last Longer. Health regeneration and longer Gunzerking is what you’re all about when tanking for the team.

and

Level 37-41 – Max out Sexual Tyrannosaurus (really?) that gives you health regeneration while taking damage. In other words you will be in god mode for real.

Also, there is a legendary shield that regenerates life (source: Borderlands 2 wiki)

Neogenator, Anshin, Legendary: Regenerates health when active. Damage to shield increases health regen rate.

Gunzerker has a couple regen skills when taking damage and when gunzerking I think. Mechromancer regens health when their mag is full with a skill and the Siren tree has one which regens more health the less heath you currently have and another which regens health for you/your party when Phaselock is active.

In addition to various skills, there's various class mods and shields that help you regen health. The NEogenator is the only health regen shield I know of, there's also the Blood of Terramorphous relic with ~.5% health per second regen. Assorted class mods also have health regen as a main effect, but these tend to be absolute values not relative to your total health, and furthermore they seem to universally be extremely underpowered, especially at high levels.

IIRC there's also a Seraph (pink) relic which regens health, but it's ridiculously tedious to acquire (as all seraph weapons are) so I wouldn't recommend it.