A PC in Blades in the Dark is in a bit of trouble. All of his harm slots are filled up, and someone's still trying to kill him. They don't care to capture or otherwise disable the character, they want his head. He's fighting back, poorly. He fails the roll and suffers harm as the logical consequence. But! He refuses to accept that consequence, and gains stress to reduce the severity (page 32). Cool.

Except the reduced harm still has nowhere to go (all slots taken), so it would get upgraded again. And here the GM has two options: either negate the consequence entirely, or essentially say the consequence is unavoidable. The former option is perfectly legal, but the character can keep refusing to die when more harm is dealt to him later. He gets a random amount of stress while doing so, but that amount can even be 0, so this could go on for a while. Whereas the latter option appears to be against the spirit of the game. 

The book talks about deciding which consequences can be reduced and which are avoided entirely, so suppose we're playing a gritty game where everything is normally only reduced.

This is a contrived situation unlikely to be an issue in play, picked for the clarity it presents - I'm trying to understand the logic of the rules. The less egregious example of resisting moderate harm with both lesser harm slots filled is quite possible.