In shorter words,

Neither of case above is about property rights.

In the first you assume it’s abandoned, if that’s true then fine, if there IS an owner who wants them to leave then they have to leave.

While your second case is something no one owns.

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It is about natural law, not the government.

Yes, if the owner wants them to leave they have to leave. But if the owner was not present for 20 years, made no protective measures and cannot be contacted, why should we assume the owner still wants the property? Especially in this age when you can have it connected to the Internet.

The conditions should be reasonably strict to avoid unjust property transfer, of course.