Questions about possible eviction

[Nate Pucel]

So long story short we have a traveling nurse staying at our rental that got some water damage when the roof was being replaced, they don't have renter's insurance (which we require in the renter's agreement they sign), water damage has been remedied and is cosmetically minimally affected and still very much in a liveable state.

They've only paid 800 of 2300 rent for October. We've been in communication about getting everything repaired until they found out the contractor said it would take approximately 4 to 6 weeks to fix the spots of drywall that have been removed and to repaint, etc, and now their responses to my texts are less and less. They've mentioned they have asthma and allergies and that's why they're upset about have to live in a place that's being repaired, so I've offered to both hold off on the repairs and reduce rent to make up for the condition of the property, I've offered to have a contractor just rough in the drywall so that the studs aren't visible and to encapsulate everything, even though everything in the cavity was removed during the remediation, but they now aren't responding to my texts whatsoever.

It's very frustrating bc the situation isn't anything I caused. The roof had to be repaired bc a tree fell on it during a storm and the roofing contractor's tarp blew off during another storm and that's how water got in, which the tenant has acknowledged. I've done everything I can think of to help them, but they're no longer willing to cooperate, seemingly. I feel like I'm at the point of have to give a 5 day notice (Illinois), but I'm also wanting to notify their nursing placement agency as they're not paying rent, and they've been late on rent 2 other months now. Am I allowed to contact their agency to notify them of this, or serve the 5 day notice to them at work in order to try and get them to pay? I'm new to being a landlord, and it's a little disheartening as this is my first tenant and I thought I was minimizing the risk of a bad tenant by renting to traveling professionals.