i occasionally find fart eggs in my runs. i think they do just fall out. i like to save them in a decorator bowl. There is so little stuff inside they dry out in no time. i got a button quail fart egg one time. Now that was teeny!
Last year we had geese sitting on nests and on eggs FAR into the year, it was my first year with 'em and we got a few late goslings, one made it but only because I rescued it - it had fallen into a hole and was treading water down there, of course the geese are all brave and deserve medals - just ask 'em - for rescuing it from ME, who was going to eat it or something. But anyway, at this time I found the odd "goose fart" egg, full size, not in a nest just .... lying out in the open.
This time around (although frankly I hope to have sold our flock by then) I know that once the season's gaggle of goslings is out and about, to be the meanie and break up the nests, take any wonky eggs and into the garden they go, and as for "goose farts", well, they make a fine omelet (unless I want to incubate them and raise 'em, although geese are wonderful to their season's school of little ones, the odd little one that comes later has a hard life, it's kinda soured me on geese, mean bird-bullies, it was all I could do not to take the little one that I rescued and keep him/her in with me and raise it myself.