This answer to Does anything orbit the Sun faster than Mercury? explains that while Vulcanoid asteroids may have been plentiful in the past, large ones have currently been ruled out though smaller ones less than about 6 km might still be there. It's difficult to observe them because from Earth it requires pointing close to the Sun, and from spacecraft that are much closer (i.e. Mercury and lower) it's really hot and difficult to do.
I think that the current limits are set by analysis of historical STEREO images, space telescopes in orbit at 1 AU designed to look at and around the Sun. A Search for Vulcanoids with the STEREO Heliospheric Imager
My understanding is that during solar system formation there were asteroids all over the place as things formed and then collided, but as some bodies became large large swaths were swept clean and some bands remained.
Have any theories been put forth explaining why the vulcanoid belt seems to be depleted of large asteroids? Is this band, while quite stable, simply not stable enough? Do some think that it simply was never populated by large asteroids to begin with for some reason?
Question: Where have all the Vulcanoids gone? (sung to the tune of Where have all the flowers gone?)