If a friend is truly unwilling to accept any conflict whatsoever or engage in a relationship based on honesty about their feelings, there isn't really anything you can do on that front. Luckily, many people do want this kind of honest relationships but don't quite know how to create them.
What you can do is foster a relationship where it's safe and okay to have disagreements. This is something that ideally starts before you and a friend have any major rifts. Be thoughtful and intentional about talking to your friends kindly, calmly and without burning bridges, if they do something to upset or hurt you. If they apologize or make it right somehow, show appreciation and allow the relationship to be healed.
Encourage them to do the same. If one of them does come to you with a concern or lets you know that you hurt or offended them in some small way, listen and take their words into consideration. Try not to be defensive, but accept that even if your intent wasn't to be hurtful, your words or actions had a negative impact from their perspective. Do what you can to make it right and respond with warmth if they allow the relationship to be repaired.
Try to create an environment where "say nothing and stew in your upset and resentment until the only recourse is to end the relationship" is not one of the more attractive options. Be a person who can take criticism with open-mindedness and grace, and give it with gentleness. Act this way about all the small moments of annoyance or hurt feelings, and when something big comes up, you and your friend will know that your concerns will be taken seriously by the other, that it's 'socially safe' to disagree, raise problems or voice your true feelings, and that your friendship might even be stronger in the end for having been honest with each other.
I have a best friend who I love more than most things in this world, and she and I are both pretty strong willed and can be emotional people. We don't have a relationship that is free of occasional disagreements and negative emotions, but our friendship remains strong because we know that if there's a problem the other will listen, care that they caused pain or annoyance, and put more importance on maintaining the relationship than on being right.