These were technically coins which were processed as smart contracts in Ethereum. Even if these coins "cease operations" their history will continue to exist in the Ethereum blockchain, forever.
>>RexM+Z3
No, as long as at least one person chooses to host a full-node (or, just a torrent containing the entire historical chain). It's exceptionally unlikely that this information will cease to exist in our lifetimes.
>>vel0ci+(OP)
This is incorrect. Terra is a Cosmos chain. Some Luna and UST exists on other chains, but these tokens represent claims to tokens on Terra.