When the conflict can be dealt with peacefully, 99 percent of the employees will usually take care of it themselves. It's when the conflict cannot be resolved by the usual methods that the trouble starts.
Sometimes, an employee is just not willing to deal with the problem. I worked with a woman for 15 years who was moody, edgy, prone to outbursts, secretive about herself, but a busybody where everyone else was concerned, thin-skinned, paranoid and had a chip on her shoulder. She routinely alienated co-workers and customers alike, but management was afraid she would file a discrimination lawsuit if she were fired, and she probably would have.
For about three months after she left, I'd start if anyone came up behind me, fearful it was her. It's not a pleasant way to work.