Synonyms leave (stop living with somebody permanently): He left his wife and daughter. She has threatened to leave me.
desert (leave somebody without help or support): I’ll never desert a friend in trouble.
turn your back on somebody(refuse to help someone that you have previously helped):
It’s not fair to turn your back on your own mother when she needs you.
neglect (fail to look after someone properly): She denies neglecting her child so far.
walk out on somebody (suddenly leave someone): She walked out on his husband and kids afterwards.