The tenant is expected to notify you, and maybe they will, maybe they won't.Because they have nowhere else to go and no funds (and usually no job),  you'll be paying for an eviction. 

Hi all, I'm looking at some single family properties in the area and there is one for sale that says the current tenants are paying $500 below market value.

You can call it 'overpriced' but others are willing to pay it, so I'd focus on finding the best deal you can find in your area, and not on a CoC return rate that may not be realistic these days. 

We current have about $500k in equity (down payment and loan pay down).

Who pays for that increase cost?

Also, I will be paying his commission because I want these units rented asap. 

Hello I recently rehabbed a sf and now I have a tenant paying $1200 per month.

I don't mind paying for a market research subscription that's worth the cost.

We have enough capital now to purchase a property and and we are blessed to have capital left over every month as well, which we typically invest in CDs.Here are our current options: 1-Buy a turnkey place that has nothing to do with mom for cash flow of $200-300/month plus potential appreciation, overall ROI of 15-20% 2- Ask mom if she would move closer to us in San Diego, buy a small place here, have zero cashflow but at least we have another property in a great appreciating market and are no longer spending the $800 on her rent3- Buy a place for her in Orlando, same scenario as above but obviously a lesser mortgage since its FL and not CAWe found a great turnkey company we liked so if we do option one I think we will use them, but it just feels like if we do that we will still be tossing away what we currently pay on her rent. 

I just got one last month that had been on the market for awhile and after moving out it's around 13% when estimating 10% Vacancy and 10% management fee, both of which I won't be paying on for a bit.