In my case, the property owner was incarcerated and there was a window of time where the family members could come forward to claim the property and I could lose the money I put in for repairs.

She pays on time, communicates with us and seems to be fine.Apparently, a former tenant, from before we owned the property, was incarcerated and has since been released.

Either look at them as “never rented before” (moving out of their parents home and starting their own independent lives) or “skip over this one” (mature adults with no prior mortgages/ ownership of real estate who are lying to you or maybe were homeless or incarcerated and are getting back on track).

I've since discovered that he has been incarcerated, with no contactable family to speak of.Does anyone have experience or strategies for contacting and getting a deal from someone in this situation?

If you think they are incarcerated - then you need to take a different approach.

I’ve also uncovered a troubling number of civil and criminal cases that have been filed against him (just in Greenville County), most of which relate to fraud and forgery-type offenses (some of which appear to have resulted in his incarceration, the last being in Dec 2015).

There are life occurrences, such as death, incapacitation, incarceration, tax audits, law suits from another matter such as divorce, estate planning, qualification for state benefits and then there are the informer types, those that know about your activities; they might be competitors, Realtors, the clerk at the title company, Uncle Ben the attorney, the loan officer who can't help but feels for the borrower and educates them then points them toward an attorney.

My client in this case happens to be a formerly violent felon; I do not believe in credit discrimination against the formerly incarcerated.

You should add wording to your lease where a tenant can designate a person to remove property upon their death, incapacitation, or incarceration. 

Before seattle changed its rules and I hired a property manager,   I used language in my qualifying criteria to basically say that if a criminal record was present it must not reflect a pattern of repeated infractions,  must not have been for any violent crime or type of crime likely to impact landlord property, other tenants, or the landlord;   any not yet completed incarceration, parole, restitution, etc must not present an obstacle to paying rent and maintaining compliance with rental agreement, and there must be evidence of stability/mitigation, e.g. gainful employment, attending school, or some other constructive activity occurring after the conviction.But again, might be good to consult with attorney OR work with a local snohomish county property manager or landlord group who know better what is going on there.Again I would also seriously consider having floor on credit score.