Tougher breaks: you hit 0 hp, you die; no death saves. But what if, as you die, you get to make one last move to swing that final combat scene in a different direction and go out in a blaze of glory? Below are some sketches for "death moves" for the baseline 5e character classes:
Some furies can only be slaked by violence. You should number among the dead, yet you rise again to heft your weapon against your foes. You continue to fight. You cannot be healed, but neither can you be killed. At the end of the battle, you fall to the ground having died a warrior.
With your last breath you sing one final, mournful dirge. Your allies are bolstered by the song and gain advantage on their attack rolls for the rest of the scene.
A holy soul never shudders at the thought of death, for you go on to a better place. Before you depart the mortal coil, you pronounce a benediction that gives your allies a stock of temporary hit points.
Some die unavenged, but not you: nature will have its revenge. The area erupts in natural phenomena that turns it into difficult terrain for your foes and harms your enemies within it.
A lifetime of bloodshed has changed the way you see the world; even as you die you see one last tactical opportunity. Before you perish you make one last, impressive maneuver that reveals your enemies' weakness in a way that your compatriots can exploit.
All your life you have resisted the temptation of the dark hadou. Now, as death approaches on silk slippers, you give in and become an avatar of disciplined destruction.
Heaven avenges its own. As you die, a glorious light fills your vision: a warrior angel come to take your place and fight alongside your companions in your stead.
Death hungers for your life, but that hunger is matched by that of the beasts who now arrive to rend and tear at your foes.
You appear to fall on the field of battle, but this feint carries the scent of finality: it was all a deadly ruse that catches one of your foes unawares and inflicts a grievous injury.
The magic that flows through your veins spills out and its power can no longer be contained. As your lifeblood ebbs away it causes a magical explosion to wrack the area, greatly damaging your foes.
Before your soul departs to serve your patron for eternity, you pronounce a lasting curse on your enemies. You foes make their attack rolls and saving throws with disadvantage for the rest of the scene.
You've kept it hidden all long, this last dweomer. As you die, you can one final spell that changes everything.