 P will maintain its own concentration at a certain level, until some other stimulus will lower it down below the threshold level, when concentration of P will be insufficient to make gene G express at the rate that would overcome the loss or use of the protein P.
This state ("on" or "off") gets inherited after cell division, since the concentration of protein a usually remains the same after mitosis.However, the state can be easily disrupted by outside factors.Similarly, this phenomenon is not only restricted to genes but may also apply to other genetic units, including mRNA transcripts.