How do you begin to help someone with abandonment issues?
The psychological wounds caused by the rejection / abandonment of a parent does not heal easily and we often carry that well into our adult life unless we specifically address it e.g. through psychotherapy.
Often people who have experienced rejection / abandonment early in life acquire an interactional style through which they try to prevent experiencing the pain of rejection again. They thus often keep people at a distance, struggle to trust others and open up and often end up living a self-fulfilling prophecy where in their attempt to prevent rejection by others they make sure that they will (when necessary) rather be in the rejecting position than being the one who is rejected. They thus easily behave in a hostile manner towards others and distance themselves from others which in the end lead to them being rejected.
The only way in which you can really help or assist is through compassion, understanding, empathy and unconditional acceptance. Through this you may create or contribute towards an emotional corrective experience for them. Your challenge is to stick with them in a compassionate way when they become hostile or rejecting - showing them that you will stay no matter what. Eventually they will learn to trust that you will not just leave or reject them.