Since you write, "stayed in the
channel", I am assuming the metal butt of the ramrod, which holds the threaded cleaning attachments, came off, and is lodged within the stock, beneath the barrel? The tip of the ramrod did not come off while loading and is stuck in the breech?
This is a good idea.
IF this doesn't work, and if the metal end of the ramrod is threaded so it's a female end.... get a long screw with a matching thread. It's likely 8-32 or 10-32. Cut off the head of the screw so all you have is the threaded shaft. Put the threaded shaft into another ramrod with a female end, with a dab or two of locktite. This is now, temporarily, a male end. Insert this into the Browning ramrod channel, and attempt to screw the male end into the stuck female end within the stock, and remove it that way. After extraction...apply a little heat and the locktite will soften and you can remove the threaded shaft and return the other ramrod to its original configuration.
View attachment 20214
Pray the reason it's stuck is not that the former owner tried to glue it in place decades ago and glued it into the stock.....
LD