If you are a leader you're going to have a decision to make and the rules aren't necessarily going to help you.
What do I mean? I mean this: when you run up against a personnel problem that has escalated you start to think about having to let the person go.
There are laws and organizational rules for all of this, and you need to follow them, whatever they are for you.
But, whatever rules you must follow, there will be plenty left to your discretion in many organizations. AND this is where we come to it: If you are a leader you're going to have a decision to make and the rules aren't necessarily going to help you.
So what should you do? My advice is to act like a human, and I will give you my guidelines of what that means:
Is anyone else doing anything? Sometimes complaining to you is all anyone's done. If that's the case you may (or you may not) owe it to the person in question to say or do something. Or you may want to make sure that others are saying something. You may need to sit in on a meeting with the employee to help.
Think about what can be done about it. There are times where remediation can help with a challenging or failing employee. Some times strong messaging, encouragement, support, or an improvement plan can help. If it can help do it.
Be aware of team impacts. When team members begin to struggle - through negative outlook, non-productive behaviors, incompetence, or material failure - you need to think about acting for the morale of your other employees. Leaving a negative or failing person in place creates drag on and possible resentment from those around the troubled person - they may not admit it all the time, but it does. Be aware of it. Don't wait to act until others have quit. This is something you have to weigh when thinking about number 2.
In my opinion, 3 outweighs all the others. But that doesn't mean you should overreact every time there is bump. But you must protect your best employees, and you certainly must protect your best employees from being impacted by those who are struggling.
How are you going to get the best from your best if you have someone around them with a negative attitude always slowing them down.