When is attempting to recover past rent worthwhile?

[Gualtiero Piccinini]

A tenant who lived in a single family home in South St Louis City moved out in early October while owing, by the most generous estimate, $2,725. She also left a huge amount of items behind, which cost me over $700 to clean up. I do have her phone number, current address (which is in Illinois, however) and SSN. As far as I know she is broke and has no income so I suspect it would be difficult to get any money out of her, unless she gets help from others.

Is this worth pursuing and if so how would you go about it?