Of course, being an attorney my answer is "it depends". As recently covered at a recent continuing legal education update it was shared that the distribution of these assets vary, and depend on the terms of the contract created by each company. But, there is an article available on the web (dated 2011) that covers some of the big ones. Do you use a beneficiary form? Does your will control? What if you die without a will? If this seems trivial, pause and reflect on the fact that it is estimated that members are estimated to be holding approximately 3.5 trillion unused miles. That is a lot of miles to pass without a little though and reflection.
Even if you do know what will happen (they pass via will) in your situation, make sure the fact you hold those miles/points/awards is known to your personal representative. If they don't know about an asset -- does it exist?
Thanks for reading, and I'll be back next week. Also, keep in mind that a blog post is no substitute for speaking with an attorney about the specifics of your situation.
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