Evicting Section 8 in the winter?

[Michael R.]

I'm not sure how everyone else keeps it together, but for the last week of each month and every day after the first that I don't receive a rent payment for a unit I start imagining the worst.  It's actually pretty stressful and my mind runs to all the various ways it can play out. 

The one that concerns me this month is a section 8 tenant that still hasn't paid her rent as of the 7th.  I gave her a small window since she communicated that she'd be sending it on the 5th and I appreciate that over the alternative, ducking my texts/calls.  This leads to my question:

If I move to evict her and win the judgement will most likely lead to her voucher being revoked.  Since it's December and this is Illinois the sheriff will not remove her and her children until spring.  Does this mean you're shooting yourself in the foot to evict someone in this situation?  Anyone experience something similar?