The LinkedIn headline is the line beneath your name. This is the most heavily-weighted line in your profile so what goes here is vital.
In your settings, you can prevent any profile updates from going to all your connections -- except if you change your picture or your headline. LinkedIn will allow those changes to alert your network.
Your photo is one thing, and it's actually a change that will draw your connections to your profile, and that's good.
But if you change your headline, LinkedIn -- let's hope they stop doing this -- will announce to your network that you have a new job! Regardless of why you change any words in your headline, LinkedIn assumes you're telling everyone you have a new job.
Clients in a job who have made such changes with no new job have to scramble to tell their connections (and coworkers!) they do not have a new job, they simply changed some words or the phrasing in their headline. And those between jobs have to race to alert their network that yes, they are still looking.
So what should go here, whether you're employed or not? Here's where I say: Your LinkedIn profile is your profile, it's your career presence online. Unless you have a special arrangement with your company, it does not belong to your company.
Thus I strongly recommend you use that line for your current and/or recent titles, and perhaps areas of expertise.
Here's an example, for a Chemical Engineer:
Chemical Engineer | Control Engineer | Research Engineer | Research Scientist
New grad? I've urged those just starting their career to do this:
Future Financial Analyst, Management Analyst | Analytics, Statistics, Research
Using the keywords of your target position is critical, but these also must be true for you, backed by successes and achievements. It's what you're known for.
Finally, your headline is a classic statement about you, even when you do change your job. It's not "Vice President of Sales at ABC Company, worldwide provider of digital widgets", it's about you and what you do well and what is your work over time. As you move through your career, you will add to it and change it.
Let's hope by then, LinkedIn will have changed its assumption that you are announcing a new job. Until then, follow the tips above and your life on LinkedIn will be simpler. And more powerful!