A plaintext private key is an unencrypted private key. Ownership of the private key means ownership and control of the assets in your wallet. A plaintext private key is different from Keystore, the partially encrypted private key file. As long as the password is strong enough, it is difficult to crack even if the hacker has Keystore.
The private key stored in the wallet is completely independent and can be generated and managed by the wallet software without blockchain or network connection.
The user's wallet address is a 42-bit address starting with 0x generated from a public key that is created from a private key (a string of 64-bit hexadecimal hash strings) with elliptic-curve cryptography.