What does soaking in a solution of baking soda do to fruit when preserving it? Last year the recipe I used for preserving whole figs involved pricking the figs with a fork and soaking them in a weak solution of baking soda. 

What is the baking soda doing to the fruit in this step? Can it be keeping the figs from disintegration (a problem with this year's batch)?

The remainder of the recipe involves boiling the fruit with lots of sugar, then putting the fruit into jars, thickening the remaining syrup and topping off the jars with that.
Alkalinity breaks down the structure of plant cell walls.  I assume the purpose of this baking soda bath is to soften the structure of the fig. That's why yours softened so much.  If you want to maintain the structure of the fig, try using an acidic bath, as acidity helps to maintain plant cell structure.