"D'un pareil soin" is a turn from the old French language and it would not be used nowadays. We could find in a contemporary translation something like this, in which the idea is not explicit as the expression has been simply omitted;
- … Le fait qu'il s'en voit si peu de bons est un signe de prix et de valeur.
Il en advient comme aux cages: les oiseaux qui sont dehors cherchent désespérément à y entrer, et ceux qui sont dedans cherchent tout autant à en sortir.
"D'un pareil soin" signifies "in reason of the the same state affairs", this implicitly stated state of affairs being the imprisonnement by means of a cage, which is also a means of isolation of the "prisoners" from the outside world. Interestingly enough, there is a chinese proverb that rhymes strangely with Montaigne's thought, and that I think worthwhile mentioning;
- Le mariage est comme une place assiégée ; ceux qui sont dehors veulent y entrer et ceux qui sont dedans veulent en sortir.
As per Littré, "advient" comes from the initial form of "advenir" (avenir) and this verb meant "échoir", "se faire"; "se faire" can be translated as "to come about".