Even if this hasn't happened to you yet it can still break your heart, can't it? Why can't life be easy and everyone be included? Good question! However, it's something we as adults have to face each and every day, don't we? The key here is, how do you pick yourself up and carry on each day? Resilience! How do we help our kids build their own level of resilience is what we need to ask ourselves.
As your child fails to achieve making a team - sports or academic or theater or whatever - reinforce their problem solving skills. We need realize the opportunity in the failure and embrace it. As you know, we start with EMPATHY. It's a sad time, let them be sad. You can even be sad with them but please don't run to the coach.
When the time is right, ask your child the rest of the problem solving questions: What are YOU going to do about it? Would you like to hear what SOME kids might do? Remember to offer your suggestions ONLY if they say yes. Then wish them luck and let them know you're there to help if they still need it.
In one case the mom said within a day or two her daughter had already decided to do another sport that was no-cut at her school She had moved on even before the mom was ready to! Resilience! Yeah!