This may seem apples/oranges, but Self-Storage and renting houses are surprisingly similar. If we have that situation in storage, we go through all the legal processes of treating the tenant as if they were just a non-paying tenant for the sole reason of CYA. It doesn't cost that much to evict; it just freezes your asset while you work it out through the courts, losing revenue. My opinion in your situation is to do the same. Treat them as though they are a non-paying tenant and legally evict them.
That's not to say that I could possibly maybe have known some people who hypothetically have skipped all that bureaucratic hassle because their gut told them the tenant is way too lazy to ever come back with some sort of wrongful eviction litigation. In that case, they just skipped to the end of the "proper" protocol. You should document all attempts at contacting them no matter what, but if you choose this quicker route, DEFINITELY document all the times you tried to reach them.
Are you sure you don't have an "out" in the lease that you can find that says that if they ___________, then they have legally abandoned the unit to you? For example, if you are unable to contact them for X days, or if the home appears unlived in for X days, then you may consider the lease voided and/or consider the home vacated?
To be fair, my thoughts are anecdotal, not legally sound :) But some things to think about.