Therein lies the problem; dying is no longer a failure. It sounds like dying is a viable goal. It becomes an upgrade.
There are several ways you could modify this idea to fit the theme better. For example, you could have a secondary goal of your game be to try and get a high score. The high score could be partly based on time, so that although you could continue on after dying, it will slow you down and impact your score. This idea interprets the theme to be "failure is an option (though not necessarily the best option)."
or maybe you create a side-scrolling platformer game. Say, for example, that falling into a pit doesn't kill you, but causes you to have to take a longer path through the level. Basically you could present the player with a bunch of hard tasks that are beneficial in some way (such as being faster), but if they fail those tasks they get an easier but less rewarding task.
Or maybe a story driven game where if the user fails a quest or something then the story could branch and go down a different path. This isn't necessarily a total "failure" for the player of the game because they get to see new content by failing, but as far as the story goes, the character in the game still failed at something. I think this is still a valid interpretation of the theme.
Or maybe you create a game such that failing does indeed cause the player to lose, but is rewarding in some other way. For example, the player might get achievements after failing a certain number of times, or they get some collectible that is otherwise inconsequential to the main game. Maybe the user gets presented with a really humorous failure screen. The idea here being that the player isn't trying to fail to complete the main game, but they don't necessarily mind failing because they get something else for it. They might even want to intentionally fail a few times so that they can see all of this side content in the game.
These are just some ideas that might help get the creative juices flowing for some.
