When you change ships does your old one disappear?

If you set your ship down right next to a crashed one (so you can easily find your ship again), then you can claim ownership of the crashed ship, scrap all of its parts for valuable elements, and walk over and reclaim ownership of your original ship. You won't lose anything.

The game seems to do a good job of remembering the state of things (e.g. which boxes have been opened, which houseplants have been farmed, etc.) even very far away from one's current position, but I don't know what its limits are, and I would be very surprised if it remembers that info after the game has been shut off.

Terrifying Update

I recently made my first multi-million unit ship purchase inside a space station. My old ship was still sitting where it had been when the purchase was complete, and as I'd not been able to fit all of my inventory into the new ship, I decided to use the above tactic to go grab the rest. When I reclaimed my old ship, grabbed the remaining items, and turned around ... my new ship was gone. My heart stopped for several beats until I realized that the game had moved it to a different landing pad. (It had been parked behind my old ship and now it was to the right of my old ship.)

So, I don't know how safe it is in general to immediately reclaim your old ship after you buy a new one. (But I still regularly use this approach on crashed ships.)

Similar to upgrading a multi-tool you lose the old one but can pull whatever attachments over at the compare screen.

Made the mistake of not transferring the first time and lost some good stuff.

I don't think the accepted answer is correct.

When I was tearing apart the upgrades on my old ship I accidentally discarded a stack of much needed Zinc.
No problem, I thought, I'll just reload my last save.
After I reloaded my last save, my old ship was no where to be found.

So if you have reloaded since you transferred ships, I don't think you are going to find your old one anywhere.

There's currently a glitch with claiming ships (2.06C) where you can lose access to your current starship if it has any movable items left in its inventory when you swap. Just make sure you empty it to your exosuit and freighter before hand.