As a recent post points out, ripe figs are squishy (and they droop in a way that birds can see from miles off).
If you want to let them get this ripe and delicious you have to protect them - if you don't you'll never taste a ripe fig.
I've tried many methods but the best and easiest by far is to use the cut-off 5l plastic water containers you probably already have to use as bell cloches in spring.
The ripening figs change colour and grow several days before they are properly ripe - these figs are always near the end of branches and the whole end with the fig can be pushed right into the open bottom of the container (it doesn't matter if the leaves get a bit crushed - they will recover).
Then get a 12-15cm plastic pot and squash it slightly to insert it rim-first into the open bottom of the 5l bottle - this will click into the ridges for a firm fit to stop birds getting inside.
Apart from the protection, this 'flying cloche' will also speed up the ripening slightly, an is particularly useful at the beginning and end of the season when ripening can be sluggish.
It doesn't even matter if you knock off some of the small figs at the end of the branch - nothing that's smaller than a golfball now will ripen before the frosts.
Cheers.