Depends on what the behavior issue is. A moral business will not want an employee who does things like what Rice did.
Let me quote you:
Businesses don’t make money by firing their best employees.
If they start paying attention to what you do away from work they run the risk of having to break that rule. So smart businesses avoid knowing what you do away from work unless it impacts work. You can Ray Rice your wife all day long, it’s only a problem for the place you work if it lands on youtube with their name attached or the jail times makes you miss deadlines.