There are two main ways to avoid someone on Facebook. One is to unfriend someone, keeping them from viewing any information you've made privy only to your friends. The second, more intense step is to block someone (you must already not be friends on Facebook). When someone has blocked you, you can't even search for his or her content. Because it can be a sign that someone is really upset with you, figuring out whether they've "hidden" you is an important first step in fixing the problem.
Compile a list of the names of the people who you think may be hiding you on Facebook.
Search for one of the names in Facebook with the search bar at the top of the screen. Type just the first few letters of the name and see if the name pops up. Names that you can see in search are not hiding you. Go through the list and cross off any people who you can see in search.
Search your messages for recent ones from the people on your list. Blocking goes both ways, so anyone who can message you is not hiding you.
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Go through the remainder of your list and think of any reasons people might be hiding you. It's possible that they've just disabled their Facebook account. Consider contacting people to resolve any conflicts through another means. Being genuine and honest will help people see that you're willing to work on anything that needs resolution.