I'd say that depends on what you want the reader to focus on. Comic book panels aren't primarily about aesthetic image composition or a realistic reflection of the world, but about directing the readers eye and conveying the plot of a story in a smooth way.
If the character is in distress because of the environment (like crossing a dangerous river or the bad guis hiding in a maze of shipping containers), then I would focus on the environment for 1 - 2 panels before fading it to the background and focusing on the characters face showing the fear.
However, if the characters distress has no direct link to the surrounding, then you shouldn't put much detail into it, because it draws the attention away from the character. You could even draw it only roughly or blurry and possibly cover parts of it with text.
You can fade the background by removing details or removing color. Removing details is easy: You mostly draw the outlines and very few additional lines. Removing color means that you give all objects in the background the same base color. Blue sky, dark blue trees, light blue mountain tops. Or orange sky with a yellow sun and yellow buildings reflecting the sunlight. The background is still there, but it's obviously less important that the character or object in a contrasting color.
In panels where you want to focus on a motion like a hand-to-hand fight, you should even leave the background completely blank. I've seen some comics where fight scenes are drawn with a very light (sky) blue background which looks very natural and doesn't distract from the action.
The same is true for key moments of a characters emotion or inner state. When a character learns something that completely changes their world (like the death of a loved one), or they lose control over their emotions (think of the Hulk), that happens inside of the character and drawing any environment would take the focus away from that inside perspective.
As to the color of the background, there are some obvious choices. Night scenes should be darker than bright sunlight, of course. If the character is blinded by some light source, you can help the reader identify with the character if this one panel is significantly brighter than the rest.
But colors can also convey emotions. Red is a classic background color for anger and rage, certain green tones can invoke a feeling of sickness and pale blue can make a scene feel cold.
You can also hint at the emotional state of a character. Bright and fully saturated colors can evoke a feeling of happyness or being energetic, while muted colors (moving towards grey in a color wheel) can convey a feeling of depression or hopelessness.
So if the caracter is mourning someone, I would keep the background mostly in muted blues, violets and greys, regardless of what it would look like in reality. Constrain yourself to a narrow angle of the color wheel to express the sadness of the scene. A more artistic approach would be to fade half of the face of the character into the background color.
If the character is injured, fighting someone or running away, I would keep the colors brighter and use more colors for the background to express the energy and adrenalin of the scene. If the background would naturally be dark, I would create a halo around the character to increase the contrast (which also increases the "energy" of the scene).