The even more curious thing about Liechtenstein is that the current territory was an afterthought to the actual dynasty. They were by origin Austrian barons with extensive estates their and within the crown of Bohemia. So actually most of their wealth and importance came from their status as subjects of the Hapsburg dynasty, rather than the Emperor per se. Modern Liechtenstein ( based on the former princely states of Vaduz and Schellenberg ) were purchased purely to elevate the house of Liechtenstein to a higher official rank ( “count” ) that would allow them to hold office in the imperial reichstag. When the Hapsburg state was dissolved, all their vast lands were annexed - except that tiny little unimportant rump they had bought in the Alps.
History is strange sometimes :).