They've simply changed their profile settings so people can't add them as a friend. The button can appear/disappear based on previous actions, for example, a denied request or blocking then unblocking a user. Your friend should still be able to send a request to you, if not, submit a help request to facebook.com/help..
Thereof, why is the add friend button greyed out?
If the add friend and follow button is greyed out of one of your friends facebook then it can only happen due to two following reasons: Because you already sent a friend request and it got rejected. So Facebook might have banned you from sending friend requests to this person.
Also, can you tell if someone blocked you on Facebook? If you see the display image of the person you're looking for, click on it. You'll be able to partially view the profile (depending on their privacy settings) if they've simply unfriended you. If you can see their name and profile picture, you can let out a sigh of relief, as they haven't blocked you.
Beside above, why can't I cancel a friend request on Facebook?
Click View Sent Requests and the list of the people you sent a facebook friend requests to will be displayed. Now, go to the name of the person you want to cancel the friend request, hover your mouse on the friend request sent and then click on the cancel request button. Note that you may need to confirm the action.
What does it mean when a name is greyed out on Facebook?
If your friend's profile picture is still visible, but his or her name is greyed out and cannot be clicked to access his or her profile, you have likely been blocked. If your friend's messages bear the name "Facebook User", rather than his or her actual name, s/he has definitely deleted his or her profile.
Related Question Answers
Does the add friend button reset?
Originally Answered: Does the 'add friend' button resets after someone declines you? Yes.What does it mean when you can only message someone on Facebook?
What does it mean when a person only has a message on their Facebook page? If you're talking about that feature where you can't friend someone, and you can only message them, then it means that person is an arrogant jerk & if you like that sort of thing, you should message them.Why are some Facebook comments GREY?
Facebook now turns spam and unrelated comments on Page posts gray to denote them as low quality to admins, while leaving the blue background on other comments. The filter will make it easy for admins to quickly sift through thousands of comments and delete spam.What happens if someone rejects your friend request?
They will not be notified that their friend request was declined, but they will be able to send you another friend request in the future. Your former friends will not be notified, but they will be removed from your Friend List and you will be reciprocally removed from their list.Why can t I add someone as a friend on Facebook?
You or the person you want to add can only get friend requests from friends of friends. One of you may have set your privacy settings to get friend requests only from friends of friends on Facebook. Ask them to send you a request instead or change your privacy settings.How can you tell if you have been blocked on FB?
A fast way to see who's blocked you on Facebook is to check your friends list. Simply put, if the person you suspect has blocked you doesn't show up in your Facebook friends list, then you've been unfriended or blocked. If they do appear in your list, then you're still friends.How do you add a friend on Facebook privately?
You can configure who can see your friends list on Facebook. To do so, go to your profile page and click or tap the "Friends" link. Click or tap the edit button, which looks like a pencil, then click or tap "Edit Privacy." In the privacy drop-down menu, choose an audience for your friends list.How can you tell if a friend request was denied?
Click the name of the person you friend requested. Look at the gray button next to the person's name. If the button reads "Friend Request Sent," the person has not yet accepted or declined your friend request. If the button reads "+1 Add Friend," the person denied your friendship request.Can you prevent someone from adding you on Facebook?
While you can't block friend requests completely, you can block the majority of the Facebook user base from sending them. Click the downward arrow located in the upper right corner of your Facebook home page next to "Home." Click "Privacy Settings" in the drop-down menu. Click "Edit Settings" next to "How You Connect."Can you resend a friend request on Facebook?
If you've got a few on your list you'd rather not wait on (or if you want to resend it to get their attention and potentially double your rejection) you can click on the “Friend Request Sent” button beside the person's name to cancel your request and free you up to send another.How can I remove Add Friend button on Facebook 2019?
Click from the top right of any Facebook page and click Settings. Click Privacy in the left column. Click Edit next to Who can send you friend requests? From the dropdown menu, click Everyone or Friends of Friends. 
