Is buying a home that has pets that live inside the home, harmful to my family members that have extreme allergies?

Thorough cleaning: Assuming the pets are now gone and the extreme allergies are to animal dander, the house can usually be sufficiently cleaned to allow living there. It will require professional cleaning of carpets (or carpet removal), cleaning of walls, window coverings/draperies, vents, furnace filter, etc. If not cleaned thoroughly, the animal dander levels may linger for months!