I guess it depends on the type of effect you are looking for. For fading into the background you can use a principle shader and using a mix of Transmission, alpha and IOR you can create a decent fade to background. You could add some textures and color ramps to feed those setting and create even more exotic fades. Then combine with a mix shader to transparent or translucent node depending on how invisible you want the object.
If you’re set on Volume(Again it would help to know what kind of effect you are looking for) you can set the emission color to the same as the color in the principle volume node. Set your Anisotropy to -0.5. Emission setting is going to be different depending on the color pallet and the affect, but usually somewhere between 0.001 and 0.2. If it’s a solid color then usually 0.05 to 0.1 work. As always other lights and background lighting will affect the color, but it gives you a good base.
