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Technically, nothing. As long as you’re not using their announced „Recover“ cloud seed feature, your crypto stays on the blockchain where it’s always been.
PRACTICALLY speaking, your risk just went up several-fold. Without Ledger, there’s no one to update Ledger Live, which is the interface to your Ledger. You should be prepared for more scams/malware/fake apps that purport to be Ledger/Ledger Live, and these will try to convince you to sign transactions or enter your seed into their fake apps.
ALSO, even if you avoid the scams, you will need to find an alternative online interface to connect to your Ledger, e.g., Electrum or another wallet. Not a major issue itself, but these situations always introduce some uncertainty and potential for mistakes/abuse. None of this is unique to Ledger btw. If Trezor goes out of business, then Trezor Suite users are going to have to sit up and pay more attention, too.