In this case, it depends on the specific situation, character and source of the luck. If it's simply a character who is unlucky without any outside source controlling this luck, it's not something that would be taken because it's not a power, just their lot in life. If it is indeed a curse that's been placed upon them somehow, that may be a different story.

For instance, a character like Nagito Komaeda (literally the first character to come to mind when it comes to luck like this) would go unchanged because it's not a power, magic or ability -- simply a pattern existent in his life with no outside influence. UNLESS I totally missed something with the new Dangan Ronpa stuff so that example may not be the best.