Even if they search for you on Facebook, they won’t see you. In the same way, if someone has blocked you, rather than simply discontinued your friendship, his name will not show up in your account’s search results.
However, if you let go of the wrong the person did to you and wish to reconnect with them, you can unblock them. Unblocking is simply undoing your blocking action. See: Can you Tell the People You’ve Blocked on Facebook | View your blocked list
Bear in mind that when you unblock people on Facebook, they won’t befriend you automatically. To reconnect with them, you’ll need to send them a friend request which they’ll need to accept.
Here you’ll see the steps you need to follow to unblocked people you’ve halted from accessing your Facebook profile.
To unblock people on Facebook, do the following;
1. Click the small triangular shape icon in the top right of any Facebook page. ( It is the small drop down next to the circle with the question mark in it)
2. Click on Settings from the drop-down menu to continue
3. Click on Blocking from the list displayed on the left side of the page that appears.
4. You will now see the Manage Blocking page
5. Navigate to the blocked user’s section, enter the name of the person you wish to unblock in the space provided and then click Unblock next to the name of the person.
Once you follow the step accordingly, the person will be unblocked immediately. See: My Blocked List on Messenger – How to Unblock People on Facebook Messenger
As a quick reminder, note that unblocking won’t automatically add the person back to your “friends list.” If you want to become friends with this person again, you’ll need to send them a new friend request. And you can also block them again after 48 hours just in case you change your mind.