Not free but close to it.
Some thrift shops have bag days where any clothing you can stuff into a paper grocery sack is on price---usually just 2 or 3 dollars. If you fold and roll tightly you can get about 20 or more 100% cotton shirts into a brown paper bag. It's a little time consuming to cut the buttons, cuffs collars and yokes off but you end up with some nice fabrics. Yards for almost nothing.
You can also advertise on Craigslist, Freecycle or in a local paper.
Most quilters will share.
There are people in my town that pass fabric around all the time. When I was making stockings for Project Santa we had a lot of fabric donated. Some of the things we couldn't use. We passed them. Some to a group that makes boo-boo bears for local hospitals to give to kids in out-patient and emergency rooms, some went to a group that makes book bags for needy children, etc.