Hello,
When I inherited my late grandparent's 1977 Chevrolet Caprice Classic 4-door sedan, the headliner was falling in it as well. Luckily, my father happens to work on appliances for a living, and one of the landlord's my father does work for referred me to a local upholstery shop that both him and his son use for their cars. The upholstery shop replaced the entire headliner in the Caprice for $150.00 + Tax. Obviously, the price may vary depending on where you live and the materials used, but that would definitely be an option that I would consider.