How long will the collection charge appear on the debtors credit history?

The debt will remain on a credit report for 7 years. 

The statute of limitations for breach of contract are four years. However, if the debtor makes a payment on the debt, the four years reset and start over from the date the last payment was made.

If your tenant's only source of income is from government assistance then your tenant is not collectable. You cannot garnish wages or levy a bank account for money received by the government such as SSI, CalWorks, Disability, ect.