We recently revised our emergency contact form so that tenants specify who has the authority to remove their belongings in the event "of an unanticiapted prolonged absence from the rental unit".  

You want to start reading a whole lot of books, especially the ones authored by Biggerpockets.

I would imagine that the authorization amount $$ is listed in your management agreement, i.e. anything over $300 will need owner approval? 

You own the airspace above your property meaning you can remove any limbs hanging over onto your property.I wouldn't remove a tree that is on their side without permission, but limbs hanging on my side I do remove.Contact your local housing authority or real estate attorney to find out what your state laws allow.

Some of the debt is their student loans, some are credit cards which some says the person is an authorized user on the account and then there are 2 auto loans.

At the end of the day, the sun will rise and set on IF local authorities want you to do this.

The tenant is receiving housing assistance through the Chicago Housing Authority.  

Will mention @Michael Boyer, author & long-time colleague who also sits on HOA boards and shouldn't miss this!

You would hold the funds in a LLC business for which you have signing authority and you could then; vest title to property in the name of the LLC and add a layer of asset protection, sign contracts, directly pay for expenses, and deposit the income produced by your property to the LLC account.You would be able to act more immediately and reduce paperwork and fees.More importantly, if you choose to work with a quality provider of such plans, you would have access to meaningful advise related to the investments you are making and compliance with IRS guidelines. 

Obviously, I would have a signed addendum authorizing this.