Dumbledore likely meant living without love or something similar.
Though there may be other things worse than death in a more general sense, when Dumbledore says ‘your failure to understand that there are things much worse than death has always been your greatest weakness’, it seems almost certain that what he’s referring to there is the Dark Lord’s inability to understand love, since he’d always believed that was the Dark Lord’s biggest failing. He’d been trying to convince the Dark Lord that love was powerful ever since the Dark Lord was a student at Hogwarts, and thought his continued inability to understand it his biggest weakness.
“Of some kinds of magic,’ Dumbledore corrected him quietly. ‘Of some. Of others, you remain … forgive me … woefully ignorant.’
For the first time, Voldemort smiled. It was a taut leer, an evil thing, more threatening than a look of rage.
‘The old argument,’ he said softly. ‘But nothing I have seen in the world has supported your famous pronouncements that love is more powerful than my kind of magic, Dumbledore.”
- Harry Potter and the Half-Blood Prince, Chapter 20 (Lord Voldemort’s Request)
When Dumbledore had to devise a way to protect Harry, he chose to use Harry’s mother’s sacrifice because he knew the Dark Lord would underestimate magic based on love.
“But I knew, too, where Voldemort was weak. And so I made my decision. You would be protected by an ancient magic of which he knows, which he despises, and which he has always, therefore, underestimated – to his cost. I am speaking, of course, of the fact that your mother died to save you.”
- Harry Potter and the Order of the Phoenix, Chapter 37 (The Lost Prophecy)
Dumbledore tells Harry when they meet at King’s Cross that the Dark Lord doesn’t know anything about the types of magic he doesn’t value and has never understood their power.
“And his knowledge remained woefully incomplete, Harry! That which Voldemort does not value, he takes no trouble to comprehend. Of house-elves and children’s tales, of love, loyalty and innocence, Voldemort knows and understands nothing. Nothing. That they all have a power beyond his own, a power beyond the reach of any magic, is a truth he has never grasped.”
- Harry Potter and the Deathly Hallows, Chapter 35 (King’s Cross)
He then tells Harry not to pity the dead, and instead pity above all those who live without love.
‘I think,’ said Dumbledore, ‘that if you choose to return, there is a chance that he may be finished for good. I cannot promise it. But I know this, Harry, that you have less to fear from returning here than he does.’ Harry glanced again at the raw-looking thing that trembled and choked in the shadow beneath the distant chair.
‘Do not pity the dead, Harry. Pity the living, and, above all, those who live without love.”
- Harry Potter and the Deathly Hallows, Chapter 35 (King’s Cross)
Because of this history, it seems almost certain that the thing that Dumbledore refers to as the Dark Lord’s biggest weakness is his inability to love, and therefore ‘your failure to understand that there are things much worse than death has always been your greatest weakness’ likely refers to this as well - he likely meant how the Dark Lord lives without love, or something similar to that.