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:
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).
If there was a material which could handle the internal stress, sure. That material probably doesn't exist.
Like a balloon exists at STP despite being internally at higher pressure, but balloons also pop. Tempered glass also exists and significantly higher pressure and likewise explodes. Often metal structures will retain some stress (sometimes quite high) after manufacture.
The amount of energy released at some of those other materials if they had the magical property of staying together... would be terrifying if popped.
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