Are there attempts to investigate phase states at negative pressure?
I think there is a little misconception here.
There are no negative absolute pressures. When someone talks about negative pressures, they are referring to values under atmospherical pressure, this is,between 0 and 1 atm.
There are many ways of creating this vacuum, and of course, that matter has been studied under these conditions, for example, this kind of negative pressures are applied to get the boiling point of substances reduced, so thermolabile compounds can be vaporized (or the solvent which contains them) under its decomposition temperature.