To be specific, what I mean is: is the following situation possible? At given temperature T, there are two substances, X and Y, such that pure X is a solid, pure Y is a liquid, and X and Y mix to form a single phase in all proportions.
The closest I could find was this phase diagram for silver and gold (two very similar metals, I suppose): http://www.crct.polymtl.ca/fact/phase_diagram.php?file=Ag-Au.jpg&dir=SGTE
But it looks like there is still a narrow region in which there are two phases.