I don't know if you've read any of the S
ookie Stackhouse novels, but she mentions a fairy door. In her books the door is actually a portal to the fairy world. There are several around the world in her books, but are later closed to protect humans from fairies. One door is left open on Sookie's property. She doesn't leave gifts for the fairies though, in fact, she dumps a dead body through said door to hide it
Aside from that, I've never heard of a fairy door, but it would be interesting to find such a thing. The way it happened in the Stackhouse novels was that if you stuck your foot in it would just disappear and go straight to the fairy world-though it'd still be attatched of course
I think, though, that it'd be a bit disconcerting to see your foot disappear right in front of you, whether you could still feel it or not