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Hey – If Ledger Live servers were to shut down, you would still be able to access your crypto assets. This is because your cryptocurrencies are stored on the blockchain, not on Ledger Live or your Ledger device. Your Ledger device holds the private keys that unlock the use of your crypto coins/tokens.
In such a scenario, you can retrieve your private key that your Ledger wallet was securing with your 24-word recovery phrase. This recovery phrase can be entered into a compatible wallet, meaning your coins are safe from loss even if you can’t access Ledger Live.
For more information, you can refer to these articles:
https://www.ledger.com/academy/what-if-ledger-goes-out-of-business