when I had my first shop, I was awarded a contract with the US Navy Base, Kings Bay, GA
for military members that had furniture damaged in shipment during their PCS transfer moves.
[the government reimburses military personnel for damaged household goods]
I have repaired some things that most people would toss in the dumpster right away.
I have repaired dozens of broken legs and arms on chairs, tables, etc.
if it is indeed not repairable, I got paid for the time it took for evaluation, and provided the
service member with a form that says "non repairable" for them to file with their claim.
for a clean break, clean up all the loose splinters so you can mend it back together.
it has to fit snug, without force, prior to any attempt at the next step.
if feasible, some parts must be removed to make the repairs as accurate as possible.
once the break fits cleanly back together, drill a 1/2" hole 3 or 4" deep in each piece so that a splint dowel
will fit in-line. mix polyester resin, insert a 3/8" wood dowel the length of the two holes.
make sure the break fits true and correct. next is the messy part. using masking tape,
tape off the parts that you do not want to get resin on.
pour the polyester resin into each hole - insert the dowel - try to contain the resin in the joint
as much as possible. it sets up quick so you have to be sure everything is true before it hardens.
there is no going back after this point.
after the resin cures and cools - remove all the mess with a rasp, files, sanding blocks, etc.
step #2 is make a dam with masking tape to fill the voids. after it cures, rasp, file and sand again.
the reason I use polyester fiberglass resin is that you can sand it smooth - you can not sand epoxy.
turn it over, do the next side the same way - and so forth until you are satisfied with the repair.
if it is a painted piece - prime and paint to match.
if it is natural wood with a clear finish - you need to have some lacquer color sticks on hand.
(several brands on the market for the same thing).
this is applied with a hot knife like warm wax - it hardens pretty hard after it is cooled.
more sanding, mixing colors, etc. lots and lots of sanding.
for a skilled craftsman, this is not a difficult task and can be successfully done.
if you have limited tools, limited experience, and limited skill level, you would be better
off taking the piece to a professional wood shop to have it repaired.
if it is not of great sentimental value - try to part it out and repurpose it for something else.
if not - put it by the curb, maybe someone else can do something with it.
Liquid Wood is a two-part epoxy product. very hard to sand.
unless you have some experience with epoxy, Bondo and other fillers, I would not use it.
this particular type of repair is pretty involved. it comes down to the budget:
what is your time worth vs what the customer is willing to pay.
if he says "forget it - keep the chair" then you can practice on it and hone your repair skills.
totally a judgement call on your part of what to do with it now.
if you want to start repairing furniture, there are tons of videos on YouTube on how to do it.
pick up some "curb finds" of broken chairs and practice on them.
back in my day, there was no YouTube or cell phones - we learned from our mentors.
jus my Dos Centavos