Assisted Living Facility Threatening My Wife Over Her (deceased) Mother's Outstanding Expenses

Location: Illinois

My mother in-law lived in an assisted living facility. She passed away recently.

My wife had power of attorney for her and helped her with financial transactions. Whenever there were decisions to be made at the assisted living place, my wife dealt with them. So they got used to interacting with my wife instead of her mother. My wife would always list her mother's name (never her own name) on contracts and any agreements to keep things separate and avoid personal liability for any costs.

When my MIL passed-away my wife tried to reach the coordinator at the assisted living place to find out when we had to have the room cleaned-out. This took place near the end of the month. The coordinator was on vacation for a week and did not return her calls, so the staff told her to wait until she got back. About two weeks later, the coordinator told her that since we were already into the new month, we owed them rent for the month.

The facility sent my wife a letter saying that we owe them the months rent (about $2500) and threatened to report my wife to credit agencies if we don't pay within a week. In the letter they sent, you can see my mother in-law's name on the bill. There is no place on the entire document where my wife's name appears.

My questions are:

1. Since bills and records only include my mother in-law's name, is my wife liable for her expenses?
2. Since my wife tried to contact the coordinator prior to the month's end but they failed to reply until after, aren't they responsible for the time discrepancy?
3. If they are capable of reporting my wife & they tarnish her credit rating, do we have legal recourse?

Thanks for reading!