Here's where you'll want to ensure your value proposition (rather than your employment status) stands out.  After all, your LinkedIn headline is prime real estate. It's displayed in nearly every interaction you'll have on the site and is the most heavily weighted field in LinkedIn's indexing 

scheme. Optimize your LinkedIn profile (especially your headline) by adding specific keywords that relate to your skill sets.

Just like your LinkedIn headline, your summary can be used to deliver a direct message to employers—referring to your value proposition first and foremost. What services do you provide as a business-of-one? The best way to accomplish this is by adding a vertical list of your skills underneath

your personal branding statement, which is basically you explaining the problem you like to solve for employers and what you would like to do next with your skills.

If your employment ended only recently, you have several options. Some users leave their LinkedIn profile as is for a few months, especially if they're technically still "employed" by receiving severance pay. Another option is to simply give your former job an end date on your LinkedIn profile.

While doing so will drop your profile's searchability (slightly), this is also the most straightforward way to show your current status.