If you are an Electrical Engineer, how can you handle a people that a hard headed personality and the company will not give an exit for that person?

Give a dose of their own medicine. Especially these people with big mouths. One thing more don't teach these people about technical. Put them into technical situation, then ask them what they could do to fix the problem or the situation, do this in front of other people, especially in front of the boss. If they could not do it. show it, in front of him, the boss and others, how can you work in technical. By doing this you could put them into shame, and they start to recognize you.

Regardless of what type a role you play ie electrical engineer, technician, lawyer, manager etc, there are leadership and management strategies and techniques that can be used in these types of situations eg. http://www.businessmanagementdaily.com/9192/six-steps-for-managing-difficult-employees

I had this problem at my former job. It was the "old" fight between a young engineer and some old workers. That is why I decide to make a team with all of those incompetence and lazy workers (but all of them with big mouth) and another one with serious workers. I was sure that they are not going to perform their duties and at the end of the day, when my boss asked about the site situation, he will go mad and gave them the first warning.

Ryan, my intention wasn't to see them fired, but because they chose not to work but to create trouble, I informed my boss, again and he fired them.