Can you inherit bitcoins without the private key? Since the private key is needed to validate ownership, how does it work when you cannot access the private key?

Say X owned bitcoins and willed it to Y, but Y does not have X's private key. Say X's estate does not want to to give access to the private key or the location of the private key is untraceable.
Y can't spend the Bitcoins. You need the private key for an address to spend the Bitcoins from that address. There's no way around it.