Is there any "permissionless" blockchain "without a native coin"? We may certainly say that a "permissioned" blockchain cannot have a native coin (or cryptocurreny) since in permissioned blockchain we need a permission to be eligible to participate for transactions validation and so having a native coin in a permissioned blockchain is not meaningful. 

However, on the other hand, can we say that having a native coin/cryptocurrency for a "permissionless" blockchain is crucial? Or is there any permissionless blockchain without native coin? In that case, how to ensure security and how to motivate miners/validators for participation in transactions validation?
Ripple is actually a permissioned "chain", even if we stretch what the definition of a chain is. It is run by validators and as far as I know, it is not permissionless (which I equate with "trustless"). 

I do not see a specific need for a permissionless network to have its own coin or token. It could in theory still be driven on top of an already-existing coin from another network. It depends alot on your proof-of-what algorithm. You could have a network that awards "miners" ETH for doing "work" even if your own network does not have its own native token, per se.