If your boss knows you are looking for employment outside of the company can you be fired?

Answers:
Yup. You don't "own" your job. Employment is an at will legal relationship: You can quit your job at any time for any reason, and by the very same token, your employer is perfectly free to decide they no longer need your services. (unless of course you have a union contract or employment contract that says otherwise, in which case you are no longer an "at will" employee)
The only time an employer is not free to fire a person for any reason is if the firing is done because of sex, race, color, religion, pregnancy, disability, etc.
But if they know you are looking to quit anyway, then it it perfectly legal for them to help you along.

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Yeap. You can be terminated at any time with or with out cause and with or without notice. If you are spending time at work job searching you would be terminated for cause.

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yes

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Yes, your employer can fire you for nothing if they want to. Most companies would prefer to catch you at something to fire you over, even if it means getting those 3 write ups first. The reason for that is to keep from having to pay you unemployment.

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If you live in a "Right to Work" state you can get fired for any reason or no reason at all. Here in washington state, they have to have cause.

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It depends upon whether you are using company time to job search or your own time and whether you are an "at will" employee or a union employee. If you are management or an at-will employee, then you can be fired for no reason at all. Looking for another job could be considered a show of disloyalty to the employer. If you are a union or classified employee, it is harder to get rid of you. Some employers don't hold it against an employee for wanting to better himself and improve his circumstances, but in many situations, if the employer finds out you are looking and you are a valued employee, he may start looking to fill your spot before you leave him in the lurch or he may offer you a raise to stay.