as ever there is no one solution - you need a list of things to try.
get a v. long quill in there - or anything else which will slide in and you can open up to jam inside it once it's in. (open top post assumption )
you might try getting it upside down and whacking it with a rubber mallet on the bb - to shock it free. presumably it's not that tight if it's just fallen all that way. if not rubber mallet hit with hammer but place something softer (piece of wood) on anything you're hitting.
like the wall plug idea but will only work if the post's not all the way down.
if your BB is sealed and your post is closed at the top you could actually hose water (or compressed air - you can use the petrol station air line if you butcher a valve right. ) into a water bottle cage hole - forcing it out. or even vacuum it out from the top if you can a hose on the top sealed well enough
ultimately i'd guess removing BB and pushing it out with something can't fail.
if you can see any of it through the water bottle cage holes you can scrape it back towards top with something sharp
(if open top post ) if not too far the J bend in a spoke will nicely catch the bottom lip of it (i use one to measure depth of stuck posts i'm sawing ). if spoke not long enough, half screw nipple on spoke then screw another spoke into remaining thread giving a double long spoke
.if it won't catch enough, put spoke down to lip and ram something in to bung up post - pusihing spoke to side of post and seat tube
(i wouldn't have the patience but) put good glue on end of a stick and ram it into the post - leave to dry and it might pull out the post .
as ever there is no one solution - you need a list of things to try.
get a v. long quill in there - or anything else which will slide in and you can open up to jam inside it once it's in. (open top post assumption )
you might try getting it upside down and whacking it with a rubber mallet on the bb - to shock it free. presumably it's not that tight if it's just fallen all that way. if not rubber mallet hit with hammer but place something softer (piece of wood) on anything you're hitting.
like the wall plug idea but will only work if the post's not all the way down.
if your BB is sealed and your post is closed at the top you could actually hose water (or compressed air - you can use the petrol station air line if you butcher a valve right. ) into a water bottle cage hole - forcing it out. or even vacuum it out from the top if you can a hose on the top sealed well enough
ultimately i'd guess removing BB and pushing it out with something can't fail.
if you can see any of it through the water bottle cage holes you can scrape it back towards top with something sharp
(if open top post ) if not too far the J bend in a spoke will nicely catch the bottom lip of it (i use one to measure depth of stuck posts i'm sawing ). if spoke not long enough, half screw nipple on spoke then screw another spoke into remaining thread giving a double long spoke
.if it won't catch enough, put spoke down to lip and ram something in to bung up post - pusihing spoke to side of post and seat tube
(i wouldn't have the patience but) put good glue on end of a stick and ram it into the post - leave to dry and it might pull out the post .