That's a great question. There's solid phases you can create at extreme pressure that remain stable or metastable at STP, like the diamond allotrope of carbon. I don't know of any examples that retain a high density at low pressure. Is it possible for something like that to exist?

There was a suggestion that hydrogen metal could be metastable at low pressure -- it would be much denser than molecular hydrogen -- but it looks like that's controversial:

https://en.wikipedia.org/wiki/Metallic_hydrogen

edit: Turns out diamond is ~70% denser than other forms of carbon, so that's sort of an example. Though its density is pretty low in absolute terms (~3.5 g/cm³).

https://en.wikipedia.org/wiki/Carbon