It’s inevitable sometimes,,, trap long enough and your traps will wind up being stolen or tossed somewhere where they will never be found.
I do utilize public ground and I’m always trying to think of ways to cut down on the theft. And yes,, sometimes I admit that I do overthink it.
On my body grip boxes I have my coni’s attached with cable,, and I use earth anchors ( pogos) and they are pretty deep into the ground and makes it pretty hard to pull up.. I use ferrels instead of s hooks… makes it tough because regular pliers can’t cut cable easily.
The same with my dog proofs… they are cable/earth anchored…
My water sets use a pogo on the top end on a sliding cable with rebar on the bottom,, my drowning end is in water at least waist deep and requires waders in some capacity to pull up..
Your regular joe isn’t going to be able to pull the system out without waterproof footwear or risk getting soaked.
My cage traps get heavy chain with padlocks around trees… pretty rare for some people to go tramping thru carrying bolt cutters.

Do you guys have other ideas you use??

I have an article I wrote but it's on the home PC- ill pot it later

Chain, welded connections, and earth anchors.

If they want it that bad, they'll at least have to earn it or come back with proper tools.

Anyone that trapped during the fur boom of late 70s through mid 80s as I did,, learned well how to hide your sets as well as your catch.

I never saw the daylight trapping during the fur boom....Checked traps, set traps, both new locations and remakes all in the dark.

Only skinned during the daylight.

I’ll remember your first sentence if before I die, anybody were to steal a trap. It’s never crossed my mind it could happen and I actually think it never will but interesting thread.

Dont set traps where people go.
It will also prevent other problems besides stolen traps.

Not many places in the eastern U.S. where people don't go.....Slide cables are your friend. You can slide a land animal just as easy as a water animal.

Slide them behind screening cover like brush piles, woods, down into ditches, etc......Works great for road visible sets, or anyplace where there is human traffic.

Use blended sets, and mouse hole size dirt holes....Muffle the disinctive clank of a steel hammer on stake drivers, rebar, etc. with a disposable piece of conveyor belt or thick leather wired to your hammer end.

Try and color your traps to match the local dirt, and smoke your snares to color & take the shine off.

Don't speak of where your trapping to anyone.