Hi,
It just means that the wood up from the bud needs recovery. That wood will eventually recover and bud out later.
So common practice by me is to wait until July to cut dead wood. Unless, a part of the stem gets moldy. If so I cut just under the moldy zone.
Last year the terminal bud on one stem of my "goutte d'or" did not leaf out. Two buds under that zone budded. Then in July, the former terminal bud started to grow...
I have the same story on my damn "Longue d'aout" this year. But now all buds have leafed out ... and all are slow to grow ... But the weather is and has been fresh here for this time of the year
so could be due to the weather ...
Each year is different with figs. New situations and challenges keep coming ... At some point just : water , fertilize, and watch them grow like they can . And don't forget to trim the cherry tree that has started shadowing the fig trees :P