Facebook. It is possible to remove and then to add again a friend without him/her finds out?

Question

A friend of mine did it with me and I do not know how.

Answer 1

Most likely your friend deactivated their account. So basically, one day you were trying to look for your friend, didn't find them, but then later they reappeared on your friend list?

Yup, they had deactivated their account. When people deactivate their account, it basically removes their info from Facebook (so you can't find them). But then when they reactivate their account, all the info gets restored and people can see them again.

Answer 2

ask your friend what he/she did