I would approve them except the judgements are a non-starter.  

@Bob is that actually legal to self-garnish once I have a judgement??

I am trusting my agent's judgement on this...I hope we don't have to evict as I really don't want to ruin the tenants ability to qualify for Section 8 and of course incur the expenses.

I'm sure the landlords that got the $82, 500 JUDGEMENT against them thought they were profit based.  

tenant A gets evicted but marries tenant B, gets a recommendation to keep yorkie for emotional support, and anyways, buys the building thru a court ordered forced sale to satisfy judgements and they live happily ever after with their hoard of 'support' animals... until tenants-turned-owners' 'loveable' pit bull mix killed a tenant's child and court ruled both community property owners were liable.. but they had no equity nor assets so thrown in prison for life - without emotional support animals nor pet visitation rights - and never invoked their conjugal visitation rights - the end!

The judge may give them some time after the judgement before you can execute the writ to evict.

As a landlord I personally would not chase after $300 dollars of lost rent, (that I created out of thin air)  even if it was totally free to get a judgement (and its not free) as it would create undue stress in my life, and waste time I could better spend elsewhere. 

Will you guys rent to tenants who have had evictions filed against them, but no judgement?

Myself I'd entertain the option to let them pay however they want, but would make a judgement call based on how they've been.  

This will certainly change the tone of the situation from one where the tenant is either evasive or combative to one where the tenant is engaged in trying to avoid a judgement against them.