Give declarer a winning option?

I've been obsessing over this for a few days now, especially since the concept came up in two hands over a very short time frame.

Say declarer has Kx opp Jx. The goal for the defense is to take two tricks in the suit. Declarer has no pitches coming, so he will have to break the suit himself.

If the A is offside, declarer cannot avoid the loss of two tricks. That means we should exit passively and wait for declarer to break the suit.

If the A is onside, then leading a card through declarer's K gives him a losing option.

Does that mean that if you're declaring, and you know that the defense has the count, and they break the suit, therefore you should go up with the K? You have no recourse if left to your own.

In turn, does that mean that the defense, knowing that the A is offside, should present declarer a WINNING option and break the suit once in a while?