Rules for selling provinces to Subject nations
(The following rules do not apply to Protectorates, which use standard Independent nation rules for buying provinces.)
Subjects will ONLY buy a province if:
They have a core on it;
They have a claim on it;
They have previously owned it;
You (the seller) have a core on it
But there's currently a bug which means they won't buy these provinces if they're outside of their own coring range. (Bug report: [1.4.1.6] Selling core to subject has hidden distance check & buggy Sell interface)
In the case of the fourth rule - where you have a core on it yourself - that core will be transferred to the subject. Meaning, you lose your core, and they gain a core.
Bug: This does not apply for Colonial Nations; CNs will not currently buy one of your Cores, unlike Vassals and PUs. I have raised a Bug Report for this.