Privacy on the Internet: Lawyers said maintain a low profile

Is it possible to keep one's name and background off the internet? I am a new widow with a good career. My husband had been sued before he passed away. The judge threw the case out as frivolous. My lawyers have said maintain a low profile or the parties will come after you. It's hard to disappear. So far, I've asked and my name has not been listed online. I do not know if I have a right to do this.

The other problem is now that everyone is Googled, employers think I never existed because they cannot find me. Is there something I can say that is truthful but not too revealing about why I am not listed as doing the work I've done?

[AFFA]

I wish to inform you that your name may appear on internet because of many reasons. In this you may request certain websites for removing your name while in some you may not. It depends as to why your name is on a website. In employment, employer checks employee status on the internet to know about the person and specially through social networking sites. However, when you go for an employment if your name does not appear on the internet then you can say that generally you do not like to use social networking sites or to have your name on websites without reason. You can further say that you prefer to have low profile by choice. As every individual has own preferences, therefore, your preference is to have a low profile.

AFF

Low profile can mean no profile, it seems. Although social networking sites allow choices, previous employers and projects often do not. If they choose to put your name on your work and pay search engines to promote it, the result can be out of your control.
Regarding future employers not finding your name (or work) on Google, Yahoo Search, etc., that can be a difficult issue. Who you are and what you've done seem to command a performance on Google or suspicions are raised.

Can one pay to keep your life off the internet? Will an employer take the time to research your past performance and projects without using the internet?