If I play Cull the Weak against a Rengar player, can he play Thrill of the Hunt on the target he chose for Cull the Weak to save it?

To answer your question: Yes, the player can use Thrill of the Hunt to "save" their unit from Cull the Weak, but it likely won't save that specific unit from dying.

Because Cull the Weak does not target, the player does not actually "choose" which unit to kill until the spell resolves. Here is the sequence of events based on the RiftJudge FAQ (ID 10077) and the game rules:

The Sequence of Events

1. Opponent plays Cull the Weak: They place it on the chain. As it does not target, no units are chosen yet.
2. Opponent plays Thrill of the Hunt (as a [Reaction]): They place it on the chain in response to Cull the Weak. They choose one of their units to banish and then re-play to a battlefield.
3. Chain Resolves (LIFO - Last In, First Out):
   • Thrill of the Hunt resolves first: The unit is banished and then immediately played to a battlefield. It enters as a "new" game object at that location.
   • Cull the Weak resolves second: Now the instruction "Each player kills one of their units" must be fulfilled.

The Final Result

Because Cull the Weak does not target, the opponent is not locked into killing the unit they originally planned to kill. They are simply required to kill one unit they control.

• If the unit they re-played via Thrill of the Hunt is the only unit they have on the board when Cull the Weak resolves, they are required to choose that unit to be killed to satisfy the spell's instruction.
• Per Rule 359.3.e.11 ("Do as much as you can"), if they have any units on the board, they must choose one to kill. They cannot choose "no unit" if a legal unit exists.

In summary: Using Thrill of the Hunt in response allows the player to move their unit or trigger "When played" abilities, but it does not bypass the requirement to kill a unit for Cull the Weak. If that unit remains their only unit, they will simply have to choose that same unit to fulfill the requirement.