Per wiki policy, Spoilers Off applies here and all spoilers are unmarked. You Have Been Warned.
The "plundering" of a Guardian's title is actually part of the World Tree's system.
The title can't actually be "stolen", but it can be "divided up" if it is the best chance of ensuring the Tree's existence. Old Seigen's statement (that he only partly inherited his title because the Greed stole the other half of it from Izaya) is only his speculation, and Izaya's title being transferred completely to Rein confirms that Shigeo was never going to succeed in plundering it from Izaya.