Voldemort was said to be very interested in the four founders of Hogwarts. He created a Horcrux from the Ravenclaw diadem, the Hufflepuff cup, and the Slytherin locket. Did he try to find a Gryffindor relic to complete the set, or did he not bother?
I can't see him giving up on such a task, but maybe there was insufficient time.
Gryffindor's sword was hiding 'inside' the Sorting Hat, but a famous family usually has some other heirlooms too.
If there are no canon answers I'd be interested in your own speculation!