1. Give up on: This implies a loss of hope or interest in something.
* Example: The team gave up on the project after repeated failures.
2. Leave behind: This implies that something or someone is left in a place without being taken care of.
* Example: The family left behind their home after the hurricane.
3. Dump (someone/something): This is a more informal way of saying that someone or something has been left behind, often in a negative or unpleasant way.
* Example: He dumped his old girlfriend for a younger one.
The best phrasal verb to use will depend on the specific context and the meaning you want to convey.