Are you a no kill shelter?

No

If the animal is really messed up (sick), or can't be adopted into a rural setting (feral), it could be put down.

From the local news paper; Jan 20, 2017 · Council Bluffs Mayor Matt Walsh is praising the agreement between the city and the Midlands Humane Society for sheltering and adopting dogs found at large in the city. ... “They are a low-kill shelter, but 99-plus percent of the time, they are able to maintain the animals until they are adopted out.”

I think so