Especially with a SPOT unit, you should carry it out. There is no reason for the owner to set one down. Usually they set it down as part of reorganizing their pack, or put set it down to send out a signal. But then they will forget it and walk away.

After my SPOT came unhooked from my pack and tumbled down a steep slope in Yosemite, I have attached it to my pack strap with two independent ties. If one fails, the other holds. And I almost never detach it from my pack -- or the above will likely occur sometime.

You should carry the spot out, contact the SPOT people, and they can find the owner via the serial number inside the battery compartment.