Just to clarify, the 1st person cares more about the other’s actions than the other’s well being.
Where I'm from (southern American English), we often call such a person a user: someone who maintains a relationship solely for the purpose of exploitation or parasitism.
But it's common enough usage to be included in Urban Dictionary, where it is adequately defined.
Two synonyms of user: gold-digger, pimp
However, user may be applied to relationships such as friendships, etc., that do not involve romantic or physical activity. They're habitually parasitic and exploitative, they'll use anyone for any purpose, if they can get away with it.
- They're users; they enjoy bragging about their son's achievements, yet constantly criticize and never give him any praise or reward for his efforts.
- She's a user; she treats her daughter like a servant, while refusing her even a small allowance or some time to herself.
- He uses his son's celebrity to make himself feel famous; he likes the attention.