I've repaired quite a few of them.
They don't seem to be any one mfg'rs problem.

Fox, Parker, Ithaca, LCS, even a very modern (2000's mfgr) Italian SxS 5 figure gun.

The most common problem that I see is that the lug itself, the rounded portion that mates to the round bbl contours is a poor fit.
They drop down and the top edge sits nice along the bbls, the part you can see. But beneath there, the contact betw the two steel surfaces can be fair to very poor.

Soft solder needs a very good parts fit for it to have any strength. With out that, it's just a layer of Lead/Tin betw the parts and you know how strong that is.

The other problem I see is often just a very poor sweat solder job in spite of the fact that there may be a good fit.
The loose lug pulled from the bbls shows some tinning as does the bbl contact surfaces. But in many areas there may be none or the surfaces were not clean and the solder refuses to do what
it's supposed to do.

The Reinforced Lug does hold on a lot better and I can think of maybe 1 that had come loose that I fixed.
The reinforcement is simply that the Lug AND the Short Under Rib normally separate pieces soldered in place, are now made as one piece.
The Lower Rib section of the Reinforced Lug is much larger and has a greater area of contact to the bbls for better solder contact.
If fitted right and soldered correctly, this will solver most of the problems.

The lug takes a lot of spring tension in some mechanisms like the J Spring snap on forend. An 80yr old soft solder joint is liable to give it up. Things do break down.
Nothing everything lasts forever no matter what the old adv used to tell the buyers.

The long bolt in the tip of the FE that runs thru to engage the front end of the FE iron is there to keep the FE Wood from pulling off of the FE Iron.
This on BTF mostly where the shooters grip is on the wood, Simple physics,,the gun recoils backwards, the wood is held so it cannot recoil with the gun like it wants to.
So the gun and FE iron pull away from the FE Wood.
The 2 screws that usually attach the FE Iron to the FE Wood can act as wedges to split the wood as it is pulled forward off of the iron.
Any small screws inserted from the FE Iron shoe into the back end of the wood are of little strength. They are often stripped on guns when you go to dis-assemble them

BTF w/o the bolt anchor sometimes have other reinforcements to avoid this problem. The Fox U shaped steel plate around the iron and inletted into the wood attempts to do the same thing.

I've fixed a few 21's (w/o the bolt and with broken FE wood) by inletting at the very end of the FE iron tang for a 3/32 square steel recoil lug ( Used up, too short 3/32 HS Steel engravers bits).
The underside of the FE Iron is milled out cross-wise for the lug just ahead of the front attachment screw. Not much room there but it fits.
Kind of a bumper hitch arrangement.
Everything reinforced and positioned, then glas bedded.
The lug transfers the recoil to the wood.

When the FE lug gets loose but has not yet pulled free of the bbl's, it will slide back and forth. Sometimes takes some effort to move it by finger power, sometimes not.
The real clue will be it's forward movement will push against the very end of the under rib.
This will buckle the rib sometimes. Others will buckle it a small amt and then detach the rib for a few inches.
All depends on how good That sweat solder job was too.

Straightening out the under rib with a kink in it is sometimes difficult.
The ones where it's detached a few inches are actually easier as you can slide something under neath that end to use as an anvil to (lightly) strike and reform the rib back to normal.
They will always need some polishing after the dent & fender work.
Resetting rib(s) & lugs usually end with at least a touch up express rust blue.
Sometimes the easy ones where you can simply clean off the lug, tin it and re-sweat solder it back into place can be done w/o any sign of a repair

Here's a couple pics from 2 or 3 lug fix'es. No particular order.
[Linked Image from i.ibb.co]
[Linked Image from i.ibb.co]
[Linked Image from i.ibb.co]
[Linked Image from i.ibb.co]
[Linked Image from i.ibb.co]
[Linked Image from i.ibb.co]
[Linked Image from i.ibb.co]