My B/X retro-clone has 5 classes. Fighter, Magic-user, Thief, Cleric and this one. It functions differently in my game (all classes have the same HD and XP progression, for example), but here is a version you can use in B/X.
The idea is that you start the game very weak but can get more powerful if you survive long enough. Idea inspired by DCC RPG, this and this. This is where I got the picture.
This assumes you're rolling 3d6 for each ability; if you're using 4d6-drop-lowest change the numbers accordingly (for example, the hopeless rolls 3d6 in order but gains 2 ability points per level until modifiers add to 9). In AD&D, you might let the hopeless change class at level 9 provided he meets the requirements!
Beware: this if for hardcore, advanced, fearless powergamers and min-maxers only!
Hit dice: 1d4.
Requirements: you must roll a hopeless character (page B13) and choose to play it. If the sum of you ability modifiers is greater than zero, change all you abilities that are higher than 12 to 12.
Combat: 0-level human (B40).
Save As: normal man (B26).
Restriction: can only use simple or small weapons (d4 damage at most). Cannot wear armor or use shields. Start the game with no money.
Special abilities: after achieving 1,000 XP, the hopeless gets one ability point and must choose a class*, starting on level 1 with all abilities and restrictions from the new class.
For each new level until the sum of all ability modifiers is 3, the hopeless gets one additional ability point.
* You may choose to be an elf, dwarf, etc. Nobody had noticed that about you before. In fact, they had barely noticed you at all.