No, figs don’t ripen after being picked. So you need to read carefully. If you are picking the figs yourself make sure they aren’t too hard and that they are easy to remove. Just lift them gently and they should begin to become unattached or feel ready to leave the tree.
Unripe figs don’t taste anything like ripe figs. Not sweet and of course as we explained in a previous article much more likely to cause allergies. Personally I don’t like them over ripe, a bit like bananas. Some people like them the way they get sweeter when they get sugary ripe. I love them straight off the tree and eaten whole!