• Age \>= 18 years old

• Patients must have histopathologically /cytologically confirmed advanced solid tumor, which is refractory to standard therapeutic options, or for which there are no standard therapeutic options. Failure of all approved therapies that have a marginal impact on survival is not required as long as the treating physician considers that treatment on study is appropriate for the subject and documents that the subject elects to defer the approved therapies

• During the dose-escalation portion, patients must have primary liver malignancy (including hepatocellular carcinoma or cholangiocarcinoma) OR a solid tumor with liver dominant disease; liver dominant disease is defined as the majority of the tumor burden being in the liver per investigator assessment AND no more than two extrahepatic sites of disease (site of disease refers to organ or system). During the dose expansion portion of the study, eligibility may be limited to one or more tumor types depending on findings from the dose-escalation phase; this will be clarified in an amendment

• Patients must have Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

• Patient must have recovered from any toxic effects of previous chemotherapy, targeted therapy or radiotherapy as judged by the Investigator to =\< grade 1 (except for alopecia). Residual sensory neuropathy =\< grade 2 is allowed. Residual endocrine adverse events (such as hypothyroidism or hypoadrenalism) that are manageable with replacement therapy are allowed

• Previous chemotherapy/radiotherapy/targeted/immunotherapy therapy should have been completed at least 4 weeks prior to start of AU409 administration, or five half-lives, whichever is shorter (except for palliative radiation therapy that should be completed \>= 14 days prior to study entry)

• Patients must have an estimated life expectancy of at least 3 months

• Women of child-bearing potential (WOCBP) and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation. A male participant must agree to use highly effective contraception during the intervention period and for 60 days after the last dose of AU409 and refrain from donating sperm during this period. WOCBP are eligible to participate if they are not pregnant, not breastfeeding, and agree to follow the contraceptive guidance during the study intervention period and for at least 90 days after the last dose of AU409

⁃ Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately

• A female of child-bearing potential is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: Has not undergone a hysterectomy or bilateral oophorectomy; or has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months)

• Patients must agree, as part of the informed consent, to undergo liver biopsy (for a subset of patients enrolled at and above dose level 4) and to provide blood for pharmacokinetics analysis

• Absolute neutrophil count (ANC) \>= 1500/mm\^3

• Platelet count \>= 100,000/mm\^3

• Hemoglobin \>= 8 g/dL (prior transfusion is allowed if completed 2 weeks prior to screening and hemoglobin remains \>= 8 g/dL)

• For patients with HCC with splenic sequestration: ANC \>= 1000/mm\^3

• For patients with HCC with splenic sequestration: Platelets \>= 70,000

• Calculated clearance \>= 60 mL/min/1.73 m\^2. Actual body weight should be used for calculating creatinine clearance (e.g., using the Cockroft-Gault formula). For subjects with a Body Mass Index (BMI) \> 30 kg/m\^2, lean body weight should be used instead

• Total bilirubin =\< 1.5 X upper limit of normal (ULN) (subjects with known Gilbert's hepatic function disease can have bilirubin of up to 2 X ULN)

• Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3 X ULN; or AST/ALT =\< 5 X ULN if patient has liver tumors

• Prothrombin time (PT)/international normalized ratio (INR) =\< 1.8 times upper limit of normal (unless patient is on anticoagulation)