I called a contractor & he mentioned that putting laminate over a concrete (moisture issues, ground floor)) would not be cost effective for a rental property.

For one house with a major moisture problem, I installed a 10-in.

So we had both slab and pier and beam in soil with high clay content and pretty extreme seasonal moisture and heat variation.

Use a primer for any type of self stick to lock the dirt in place(Glue doesn't stick to dust and never EVER mop the subfloor as it puts moisture back into the wood/concrete that might take days to wick out )Good Luck

The termite and moisture inspection didn't even mention that particular floor, and I had another mold remediation expert come in for a full look-through, and he didn't note any mold there either.

His recommendation to me is prior to renting your unit out, get documentation of moisture readings on the floors, walls, and air.

I am assuming I need to hire a water leak detection company to use some sort of moisture detection equipment.

The joist has swollen from all the constant moisture. 

It was built in the 1960's and apparently the moisture has caused the flooring to rot and has given way.  

No visible water, probably just moisture coming in from the foundation.