A person who feigns sickness to avoid responsibility -

• 'A person who feigns sickness to avoid responsibility' is called - Malingerer.

• Malingerer (Noun)
English Meaning: A person who pretends to be ill or exaggerates their illness to avoid work, responsibility, or duty.
Bangla Meaning: অসুস্থতার ভান করা ব্যক্তি; দায়িত্ব এড়াতে রোগের অভিনয় করে এমন ব্যক্তি।

Other options:
ক) Concubine (উপপত্নী; রক্ষিতা): A woman who lives with a man but has a lower status than his wife, especially in a polygamous relationship.

খ) Hypocrite (ভণ্ড; ভণ্ড তপস্বী): A person who pretends to have moral standards or beliefs to which their own behaviour does not conform.

ঘ) Truant (ভবঘুরে; অলস): A person, especially a student, who stays away from school without permission or a valid reason.

Source:
1. Cambridge Dictionary.
2. Accessible Dictionary by Bangla Academy.