Can tapeworm infection become systemic? can it invade the subcutaneous tissue (face, extremities, torso) in the form of swelling, tape-like drainage?

Possible : If the immune system is weak due to chemotherapy , HIV and ETC,it's very well possible the Tapeworm becomes disseminated. Although it's more common in cysticercosis, a pork tapeworm. Please see an Infectious disease doctor.

Can be serious: Pork tapeworms in particular can migrate to other parts of the body and cause damage in the liver, eyes, heart, and brain and these infections can end up being life-threatening.Otherwise we usually see nausea, weakness, diarrhea, abdominal pain, loss of appetite OR hunger,fatigue, weight loss, and vitamin deficiencies. Roundworms and hookworms are more likely,I believe,to cause cutaneous symptoms.