In Situ Immunomodulation With CDX-301, Radiation Therapy, CDX-1140 and Poly-ICLC in Patients w/ Unresectable and Metastatic Solid Tumors

Inclusion Criteria:

* Have clinically or pathologically confirmed diagnosis of unresectable and metastatic melanoma, cutaneous SCC, basal cell carcinoma, Merkel cell carcinoma, high-grade bone and soft tissue sarcoma or HER2/neu (-) breast cancer with no curative treatment options.
* The unresectable disease to be irradiated and injected with medications must be located in breast, dermal, subcutaneous, or soft tissue, or lymph nodes with the longest axis of the tumor 2-7 centimeters, and should be considered safe for injection by the investigator.
* The metastatic disease must be measured per irRECIST criteria.
* Patient must have lesion that can be biopsied and is willing to undergo the procedure as part of the protocol.
* Have an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 1.
* Participants of child-bearing potential and men must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.
* For patients with history of radiotherapy to the same location that will be treated on study, he/she will be eligible only if the prior radiation dose was under or equal to 68 Gy total and delivered more than 6 months prior to planned re-treatment. (The cumulative dose received to the irradiated area will be no more than 87 Gy total, including a maximum of 68 Gy allowed from prior treatment course.)
* Patient requires the use of radiation therapy to the target lesion of palliation of symptoms and/or achieving local control as part of standard of care as deemed appropriate by treating radiation oncologist.
* Patients must agree to radiation to the tumor.
* Any line of therapy allowed, radiologically or clinically confirmed progression on prior therapy
* Must have adequate organ and marrow function present as defined below:

  * Platelets \>= 100,000/uL
  * Hemoglobin \>= 8.0 g/dL
  * Absolute neutrophil count (ANC) \>= 1500/uL
  * Total bilirubin =\< 1.5 X institutional upper limit of normal (ULN)
  * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional ULN.
  * Creatinine =\< 1.5 X ULN OR creatinine clearance \>= 50 mL/min per Cockcroft-Gault equation for patients with creatinine levels greater than ULN.
* Participant or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure.
* Patients must agree to injections of CDX-301, CDX-1140, and poly-ICLC.
* Patients must agree to appropriate clinical monitoring to receive the study regimens.
* Patients must agree to photos of tumors and use of the photos for publication.
* Patients should have an administration site for all injections that is free of potentially complicating dermatologic conditions such as rashes.

Exclusion Criteria:

* Patients currently treated with systemic immunosuppressive agents, including steroids, are ineligible until 3 weeks after removal from immunosuppressive treatment. (inhaled steroids are allowed)
* Patients with HER2+ breast cancer
* Concurrent use of targeted therapy including CDK4/6, mTOR, PIK3CA, PARP, BRAF, MEK, hedgehog inhibitors or chemotherapy (endocrine therapy is allowed).
* Targeted therapy including CDK4/6, mTOR, PIK3CA, PARP, BRAF, MEK, hedgehog inhibitors, chemotherapy, or immunotherapy within 2 weeks prior to first dosing of study agent. (endocrine therapy is allowed).
* Patients with active or history of autoimmune disease or history of transplantation except for the patients with Graves' disease with ablative therapy of total thyroidectomy.
* Patients with history of (non-infectious) pneumonitis/interstitial lung disease, including grade 1 pneumonitis (asymptomatic; clinical or diagnostic observations only; intervention not indicated).
* Patients with prior history of acute myeloid leukemia (AML) or known FLT3 aberrations
* Pregnant or nursing female participants.
* Unwilling or unable to follow protocol requirements.
* Patients with known serious mood disorders. (Major depression diagnosis is an exclusion: Other stable mood disorders on stable therapy for \> 6 months or not requiring therapy may be allowed after consultation with principal investigator \[PI\]).
* Cardiac risk factors including:

  * Patients experiencing cardiac event(s) (acute coronary syndrome, myocardial infarction, or ischemia) within 3 months of signing consent.
  * Patients with a New York Heart Association classification of III or IV.
* Patients with uveal melanoma.
* Patients with uncontrolled diseases other than cancer may be excluded if after consultation with PI and research team it is decided it might affect the treatment efficacy or toxicity.
* Evidence of current drug or alcohol abuse or psychiatric impairment, which in the investigator's opinion will prevent completion of the protocol therapy or follow-up. Specific testing is not required, however may be done as clinically indicated.
* Any condition which in the investigator's opinion deems the participant an unsuitable candidate to receive study drug.
* Participants with symptomatic known brain metastases \< 4 weeks from radiation treatment should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events.
* Other invasive cancers diagnosed \< 3 years back that required systemic treatment. If diagnosed with other invasive cancer \>= 3 years, should have complete recovery from all systemic toxicity except neuropathy, vitiligo, alopecia, and endocrinopathies on stable hormone replacement therapy.
* Live vaccines within 30 days prior to the first dose of trial treatment and while participating in the trial. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster, yellow fever, rabies, Bacillus Calmette-Guerin (BCG), and typhoid vaccine.
* Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies).
* Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected).
* Current use of anticoagulants (warfarin, heparin) at therapeutic levels.
* Patients who have had stroke/TIA and DVT/PE within the last 12 months.
* Patients at risk for impending visceral crisis of the liver and lungs as follows, or any condition which in the patient's primary treating oncologist's opinion deems the participant an unsuitable candidate to receive study drug:

  * A visceral crisis of the liver exists when bilirubin levels increase very rapidly (\>1.5 times the upper limit of normal) without the presence of Gilbert syndrome (i.e., Meulengracht syndrome) or a biliary tract obstruction.
  * A visceral crisis of the lungs can be assumed when dyspnea at rest increases more rapidly and cannot be relieved by pleural drainage.
* Radiation induced angiosarcoma.