31 CFR §363.165

1. (a)Unmatured savings bond. When the conversion is approved, an unmatured savings bond that is registered in the name of the TreasuryDirect ® account owner as a single owner, either coowner, an owner with beneficiary, or an entity, will be released to the account owner's conversion linked account.
2. (b)Matured savings bond. A savings bond that has reached final maturity and is registered in the name of the TreasuryDirect account owner as a single owner, either coowner, an owner with beneficiary, or an entity, will be converted to a book-entry savings bond and automatically redeemed. The redemption proceeds will be used to purchase a zero-percent certificate of indebtedness in the account owner's name in the primary account.