Other than generating a small set of known seeds, some signature formats (including ECDSA, which is used for many cryptocurrencies) also allow exfiltrating data through some of the values they consist of and which are required to validate them.

If the wallet uses deterministic ECDSA, or the algorithm used is deterministic by definition (such as EdDSA), this can be detected, but doing so requires validating some generated signatures on a second, trusted device.