A Study About the Long-Term Safety of TAK-881 in People With Primary Immunodeficiency Diseases

The main aim of this study is to learn if TAK-881 is safe and well tolerated during long-term use in adults and children with PIDD who are eligible and completed study TAK-881-3001 (NCT05755035).

The participants will receive the first dose of TAK-881 immunoglobulin (IgG) infusion at the same dosage as the last dose administered in study TAK-881-3001 (NCT05755035). After the first TAK-881 infusion in study TAK-881-3002, the dosing interval (can be adjusted by participant/caregiver) and/or the dose of TAK-881 can be adjusted by the study doctor to every 2, 3 or 4 weeks at scheduled site visits.

Participants will visit the clinic every 12 weeks until the End of Study (EOS) visit.

The study consists of two Epochs: Epoch 1 and Epoch 2. In Epoch 1 eligible participants will have the opportunity to receive TAK-881 for a minimum of 6 months. After 6 months in study TAK-881-3002, the results of the anti-rHuPH20 binding antibody assay from either study TAK-881-3001 (NCT05755035) or study TAK-881-3002 (Epoch 1) will be used to determine the next steps in the study:

* Epoch 1: Participants with an anti-rHuPH20 antibody titer less than \[\<\] 1:160 will complete the EOS visit on the day of the first non-investigational product (IP) infusion following Study Visit Week 25.
* Epoch 2: Participants with an anti-rHuPH20 antibody titer greater than or equal to \[\>=\] 1:160 at any time point during Study TAK-881-3001 (NCT05755035) and/or study TAK-881-3002 (Epoch 1), will continue with an additional two years of TAK-881 treatment and undergo safety follow-up and will complete the EOS visit on the day of the first non-IP infusion following study Visit Week 121.

Eligibility Criteria:
Inclusion Criteria

Participants who meet ALL of the following criteria are eligible for this study:

* Participant must have completed Study TAK-881-3001 (NCT05755035).
* Participant/Participant's parent(s)/legal guardian(s) is/are willing and able to comply with the requirements of the protocol.
* Participant/Participant's parent(s)/legal guardian(s) has/have provided informed consent/assent (if applicable), including providing consent for use of the investigational medical device, prior to the initiation of any study procedures.

Exclusion Criteria

* Participant has a serious medical condition such that the participant's safety or medical care would be impacted by participation in this long-term follow-up study.
* New medical condition that developed during participation in Study TAK-881-3001 (NCT05755035), that, in the judgment of the investigator, could increase risk to the participant or interfere with the evaluation of TAK-881 and/or conduct of the study.
* Participant has participated in another clinical study involving an investigational product (IP) or investigational device within 30 days prior to screening (with the exception of Study TAK-881-3001 \[NCT05755035\]).
* Participant is scheduled to participate in another clinical study involving an IP or investigational device during the course of this study.
* Participant is a family member or employee of the investigator or the investigator's site staff.
* Women of childbearing potential who meet any one of the following criteria:-

  1. Participant has a positive pregnancy test.
  2. Participant does not agree to employ a highly effective form of contraception for the duration of the study.
* If female, participant is pregnant or lactating at the time of screening or intends to become pregnant or begin lactating during the study.