People can unfriend you, or remove you from their list of friends, on Facebook. They can also hide, or block, you. This means you can't see any of their information or try to re-add them as a friend on Facebook. When people disable their Facebook account, either temporarily or permanently, you also won't be able to find them or friend them. Before becoming concerned, try a few tips to see if they've blocked you.
Click "Messages" on your Facebook homepage. In the "Search Messages" bar, start typing the name of the person for whom you're looking. When his name pops up, click on it and all messages from him appear. If you've received any messages from him since you've had trouble finding him, you are not blocked; blocking also prevents him from seeing or contacting you.
Search for the person's name in the search bar at the top of Facebook. If she shows up, you're not blocked. Blocking prevents you from seeing her at all. If you can't see her, you might not be blocked; she might just have her privacy settings so that only friends or friends of friends can find her.
Contact the person through another means if you think he might have just disabled his account. If you have his email address or phone number, consider sending a message asking if you upset him in some way. Especially if you've had an argument, sometimes a more real-life contact can show that you care about the friendship.