First of all giving power of attorney to a third party -- the "attorney in fact" - does NOT divest the person who granted the power of his or her own rights to act for himself or herself. This applies whether the power granted is a General or Limited power of attorney.
The principal -- the person who grants the power of attorney, let's call him or her X -- even can name 10 separate people, each as a power of attorney. While EACH of the named attorneys-in-fact would have the power to act for X, X still retains the power to act for him or herself so long as he or she is mentally competent. (If the power is not a durable power of attorney, it becomes ineffective upon the principal losing competence.)
With a General Power of Attorney X gives the named attorney in fact very broad powers to act for him or her in virtually any manner or thing that X could have acted for him or herself.
With a Limited Power of Attorney X typically gives the person named only certain specific powers -- and the person named can do only those things set forth in the power itself, such as sign a lease, or execute a deed, or act from May 1 to June 30.
If the person named attorney-in-fact starts acting in a manner X does not like, or X just changes hir or her mind, X can generally REVOKE the power at any time, orally or in writing, and then the person named as the attorney in fact loses all legal right to act.
People and institutions relying on the power of attorney often require the person named as attorney-in-fact to certify that he or she still has the power and that it is in effect and has not been revoked, the attorney in fact would be committing fraud by acting on the basis of the power.