If the tenant vacated without being locked out by the Sheriff, a Notice of Belief of Abandonment must be mailed to the tenant's last known address and the tenant is given 18 days to claim the property. During this time period, the Landlord is obligated to store the property in a safe place, either in the rental unit or a storage facility. If the tenant shows up to claim the property, reasonable storage charges can be demanded, but it is usually not worth the Landlord's trouble to pursue the matter since most Landlords simply want to end all dealings with the tenant. Under no circumstances may the Landlord hold the tenant's property hostage by demanding that the tenant pay past due rent or other charges. This could trigger a lawsuit by the tenant for conversion (stealing) his or her property. Always take an inventory of the personal property and take pictures or a video tape of the items.
If the property appears to have a fair market value of less than $300, then it can be disposed of by the Landlord after the 15 or 18 day period. If the property is worth more than $300, the Landlord must auction the property through a public sale. The notice of the time, date and place of the auction must be published in a newspaper of general circulation once per week for two consecutive weeks. The auction can then take place five days or more after the last notice was published.
So..I would remove the items to safely store somewhere, begin preparation of the unit to re-rent including changing the locks and wait it out the 18 days to be safe. I personally would ALSO POST this notice on the door as well as mail it.
That being said..you have some other options to look at first. Contact their Section 8 case worker, explain the situation and ask for contact info and/or for them to contact and then followup in a few days. This ON TOP OF the formal process above. Also use info on application to try cell numbers, contacts, etc.
Almost 30 years ago I was "framed" by a horrible tenant who left some TRASH in a locked garage. After two weeks we busted off the lock (they left apartment totally empty and had moved at end of notice) and threw away the trash...they filed suit. There are "serial" tenants out there that do this. Most likely they could care less and just left "junk" behind but you need to be safe rather than sorry. Take pictures of every item you remove to store and make an dated inventory. Be sure to look for their keys in weird places in the unit, under the mat, in kitchen drawers, etc. As far as charging rent for this period..it is "gray" in the courts..usually only works to THREATEN such to GET the keys back (which you should do through case worker, cell phone, contacts) but not in actual practice...