Thank you, Samba. If there could be help on the way...
The shelter's web page
Springfield-Greene County Health Department - Animal Control has much information, just checked it. They seem to work hard to place dogs in rescue, and they do check rescue organizations. Downloaded the pdf for rescue organizations under 'Common Questions'. On holding time:
"Dogs found running at large must be held for at least five days and this must include a weekend before they are eligible for rescue. Owner-surrendered animals are available for rescue immediately. Because of the small size of our shelter the maximum time we will hold an animal for a rescue organization is 10 days from the date the animal was impounded."
Since it says she was found on the 25th, she would only have until Monday the 30th, plus another five days if a rescue works on pulling her.
This pdf also states that C.A.R.E., one of the two local rescue organizations the shelter works with, typically comes in on Fri and Mon afternoons to tag dogs for pull, so they will have seen her on Friday afternoon and have some information on how she presents. Shelter also has an attending vet listed.
This one brought me to tears, too. The suffering, and also the indignity. Poor dear dog.