A verifiable credential of a natural person (user) is stored off-chain as it is personal data. The subject of the credential is the Decentralized IDentity (DID) attached to the wallet. This identity is protected by a private key stored in the wallet aside the crypto privates keys.
Basically Beacon is used to initiate a Self Sovereign Identity standard protocol to request or present verifiable credentials/ verifiable presentations to issuers or verifiers. Other protocols like OpenId 4 SSI or WACI exist.