Long-term Safety and Efficacy Study of DX-2930 (SHP643) to Prevent Acute Angioedema Attacks in Patients With Type I and Type II HAE

Inclusion Criteria: * Male and female HAE participants who are 12 years of age or older at the time of screening * Documented diagnosis of HAE (Type I or II) based on 1. Documented clinical history consistent with HAE (subcutaneous or mucosal, nonpruritic swelling episodes without accompanying urticaria). 2. Diagnostic testing results obtained during screening (or a prior DX-2930 study) that confirm HAE Type I or II: C1 inhibitor (C1-INH) functional level less than (\<) 40 percentage (%) of the normal level. Participants with functional C1-INH level 40-50% of the normal level may be enrolled if they also have a C4 level below the normal range. Participants may be retested if results are incongruent with clinical history or believed by the investigator to be confounded by long-term prophylactic (LTP) use. (It is understood that C1-INH therapy may alter the lab results of C1-INH assessments; therefore, the investigator's discretion in collaboration with Medical Monitor is advised for proper documentation of eligibility). 3. At least one of the following: Age at reported onset of first angioedema symptoms less than or equal to (\<=) 30 years, a family history consistent with HAE Type I or II, or C1q within normal range. * A historical baseline HAE attack rate of at least 1 attack per 12 weeks * Adult participants and caregivers of participants under the age of 18 are willing and able to read, understand, and sign an informed consent form. Participants age 12 to 17, whose caregiver has provided informed consent, are willing and able to read, understand and sign an assent form. * Males and females who are fertile and sexually active must adhere to contraception requirements for the duration of the study as 1. Females (NOTE: Female rollover participants (those who previously participated in Study DX-2930-03 \[NCT02586805\]) of childbearing potential may continue to use the birth control method used during Study DX-2930-03 (NCT02586805).) of childbearing potential must agree to be abstinent or it is recommended to use highly effective forms of contraception from the screening period through 30 days after the final study visit. This includes stable doses (for 3 months prior to study screening) of combined estrogen and progestin-containing hormonal contraception associated with inhibition of ovulation (oral, injectable or implantable), progestin-only hormonal contraception associated with inhibition of ovulation, intra-uterine device (IUD, all types) or intrauterine hormone releasing systems (IUS). Notes: 1) A female whose male partner has had a vasectomy must agree to use one additional form of medically acceptable contraception. 2) Use of a male condom with or without spermicide or cervical cap, diaphragm or sponge with spermicide or a combination (double barrier methods) are not considered highly effective. 2. Females of non-childbearing potential, defined as surgically sterile (status post hysterectomy, bilateral oophorectomy, or bilateral tubal ligation) or post-menopausal for at least 12 months do not require contraception during the study. 3. Males, including males who are surgically sterile (post vasectomy), with female partners of childbearing potential must agree to be abstinent or else use a medically acceptable form of contraception from the screening period through 60 days after the final study visit. Exclusion Criteria: * Discontinued from DX-2930-03 (NCT02586805) after enrollment for any reason. * If rolling over from DX-2930-03 (NCT02586805), presence of important safety concerns that would preclude participation in this study. * Concomitant diagnosis of another form of chronic, recurrent angioedema, such as acquired angioedema (AAE), HAE with normal C1 inhibitor (also known as HAE Type III), idiopathic angioedema, or recurrent angioedema associated with urticaria. * Dosing with an investigational drug (not including DX-2930 or other HAE therapies) or exposure to an investigational device within 4 weeks prior to screening. * Exposure to angiotensin-converting enzyme (ACE) inhibitors within 4 weeks prior to screening or any newly initiated or dose modification of estrogen-containing medications with systemic absorption (such as oral contraceptives or hormonal replacement therapy) 3 months prior to the screening visit. * Unwilling to discontinue use of long-term prophylactic therapy for HAE (C1-INH, attenuated androgens, or anti-fibrinolytics) within 3 weeks after starting DX-2930 treatment. * Any of the following liver function test abnormalities: alanine aminotransferase (ALT) \> 3x upper limit of normal, or aspartate aminotransferase (AST) \> 3x upper limit of normal, or total bilirubin \> 2x upper limit of normal (unless the bilirubin elevation is a result of Gilbert's Syndrome). * Pregnancy or breastfeeding. * Participant has any condition that, in the opinion of the investigator or Sponsor, may compromise their safety or compliance, preclude successful conduct of the study, or interfere with interpretation of the results (eg, history of substance abuse or dependence, a significant pre-existing illness or other major comorbidity that the investigator considers may confound the interpretation of study results).