My daughter desperately wanted to buy when the market crashed here in CA, but couldn't figure out how to save enough for a downpayment. 

I would run out the door.You'll only end up with desperate applicants willing to play your game to get into your rental. 

But if your goal is tenant retention, then you are best served by first conducting a rent survey to see what your local competition is offering for units that are on the market now; there could be a desperate landlord willing to drop rent below market, and your tenant could jump at that. 

When I lived in Davis, CA, the town was so desperate for additional student housing, that they changed the rules and encouraged people to convert their garages, etc., to be used as rentals, with the students in mind.Also, I've found in CA that in-law apartments are normally allowed for family members.As a senior now, myself (59), I can tell you there is a great need for what you're talking about. 

I don't act desperate but state it more as a matter of fact.  

Red flag #3.Unless you are desperate I would keep looking.

Something just smells fishy and desperate here.  

If you're seller isn't completely desperate they probably won't take a rubber band and some string from your pocket as the escrow deposit. 

If your rent is too high and shes the only applicant willing to pay it than that tells me she is desperate for some reason. 

You learn if they show up on time, if they bring someone who speaks for them instead of being able to speak for themselves, if they show up with an entourage that reeks of pot, you can walk them out to their vehicle to see if it's full of trash and filthy, if they smell of smoke, if they are a couple and argue about everything loudly, if they have screaming, unruly children, if they don't ask about normal things like where is the laundry, what's the parking situation, how big are the closets...all things that point to someone desperate.