When creating a new solo character, they will start the game with the shared gold/shard/glyph inventory as a previous solo character, assuming the new character was created in the same game mode (solo+hc, solo+masochist+hc, etc) and has the exact same name as the previous character. This works even though the previous character had been deleted.
I personally saw this happen in solo+masochist+hardcore, but I assume it works with other solo modes as well.