The description of Regenerate states:
You touch a creature and stimulate its natural healing ability. The target regains 4d8 + 15 hit points. For the duration of the spell, the target regains 1 hit point at the start of each of its turns (10 hit points each minute).
The target's severed body members (fingers, legs, tails, and so on), if any, are restored after 2 minutes. If you have the severed part and hold it to the stump, the spell instantaneously causes the limb to knit to the stump.
So as an example, instead of Death Ward, a Cleric casts Regenerate on a Fighter going into battle where they are hopelessly out matched.
The Fighter puts up a good fight, but brought to 0-hp, then two point-blank attacks mean immediate 4 failed death saves, all within a single round of combat. Therefore the Fighter is "permanently dead".
But can Regenerate bring them back?
A dead body is considered an "object", not a "creature". But the spell was cast while the Fighter was alive and thus a "creature" and can be a valid target of the spell. Beyond the casting, the spell only says "target". So it should no longer care about whether the Fighter is a creature or a bloody, dismembered corpse.
So every round the Fighter stands back up with 1-hp saying, "I can do this all day." Or does death invalidate the target as they no longer have a "natural healing ability"?
Best Answer
No
All healing spells including Regenerate add hitpoints. They do not bring a dead body back to life.
There is no rule saying "if you add hitpoints to a dead body, it becomes alive". Moreover, not always death implies the creature must be at 0 hitpoints. For instance, Power Word Kill kills a creature without lowering its hitpoints at all.
Being dead or alive in D&D 5e is a separate state, it correlates with current HP but not directly depends from them. A spell can bring from the dead only when its description says that.
What is different about it is that Regenerate definitely helps you to automatically survive death saving throws. If you're down and unconscious but still alive at the start of you turn, you regain consciousness with 1 HP left.