Rules and practices differ from one country to the other so it will be very difficult to provide a comprehensive answer. Some European countries (e.g. France or the UK) do require a medical exam for immigrant visas but as far as I know the focus is on a limited number of contagious diseases, especially tuberculosis.
For example, in the case of France, applicants should be up-to-date in their vaccines following French regulations (mostly relevant for children) and have to undergo a basic physical (including an X-ray of the chest but no blood test). Formally, the visa can be refused if a person is infected with one of the diseases listed in the WHO's 1969 International Health Regulations (that's the plague, cholera and yellow fever) or if they have TB or a mental ailment that make them dangerous to others and they refuse treatment. So it does not sound like your friend's problem would preclude him or her from getting a visa there.
That said, getting a visa is often very difficult, even for perfectly healthy people. You can expect a lot of bureaucracy and arbitrariness and unless your friend falls into some specific category (e.g. highly qualified professional or family member from a citizen), it's virtually impossible to get a long-stay visa for the European countries I know about.