So...my driver-side, rear tire just up and fell off the other day.
Looking at the damage, it looks like it snapped off a piece of the axle-shaft.

Are axle-shafts easy to find?
I've looked in the catalogs for the places close to me, but they don't even offer axles to begin with.

Also, just a double-dose of I don't know jack:
I put the car in gear, there was a loud THUD once I revved, and then the car would no longer go into gear.
I'd move the shifter, and nothing. No kick-back, no resistance in the movement, just smooth slide. This is a transmission issue, is it not? (My mechanic seems hellbent on not even checking the transmission)

 

If you have not good at troubleshooting and turning wrenches, I would think about take your car to a good shop. Wheels falling off and axles breaking are pretty serious...especially if you are not planting 100s of ft*lbs of torque. Something is wrong. As for where to get axles, Moser and Strange make good after market rearend parts while Nation Parts Depot cares OEM/stock replacement stuff.

 

as above. but you can check while someone has your car in gear if the driveshaft is turning. Put it this way. if the axle is broken and you have an open rear you mighst just spin the carrier. in any case the car should go to a garage. breaking axles is not really something common for a I6

 

Here's a dumb question:
Would pushing the car while it was stuck in park break the axle?

 

Only if it were ready to go to start with. You'll slide the tires til the rims melt off pushing one with a good axle. This one probably caught a curb or some other serious shock at some point in its life. Metal fatigue and some form of shock load are the most likely culprits. Metal fatiques with age and heat. Shock happens with hitting holes and stuff along with slamming it into gear or slamming it into park while moving. Generally, this breaks other things such as transmission parts and u-joints, but the weakest link will go first.

Just a heads up, but I understand this is a 7"? I'm getting rid of mine (complete rear end) should anyone be interested. It's not free and I won't part it out, but someone might find a use for it. I "think" it's 3:1 gearing, but I've only fumbled with checking it out of boredom one day.

 

I'd definitely get the the situation looked at. It is doubtful that something external cause this to happen like hitting a curb, etc. A likely issue could be a bad axle bearing that caused the axle to get hot enough to become brittle and snap. Not that uncommon on other cars, especially Caddies, but a bit unusual for six cyl Mustangs. If that occurred there could be more damage that will need to repaired.

 

A broken axel will cause the car to not go, so that is most likely the problem with that. If you have a 4 bolt 6 cylinder rear end you can pick those up on Craig's list for next to nothing. I would not pay more than $50 for complete rear end.