You may have to evict which is generally the course it goes but do something/everything (legally available) to cure this quickly. 

Generally in Illinois, the Tenant does not have the right to cure the lease violation and stay in the property.

Possibly break loan covenants and can't cure default, lender takes back property.  

Lenders stopped allowing rent by the room due to modifications done to the property resulting in functional obsolescence and significant cost to cure in the event there was a default and they needed to foreclose on the home and resell it, given that the main buyer pool for single-family homes are primary occupants. 

In my state, the notice gives the tenant 3-days to cure the default before eviction begins. 

Most leases have a clause that state that she has to keep the pipes from freezing.You can give her a cure of leave notice.

See the chart from Fair Isaac Company (FICO) below: FICO Score Pct of Population Default Probability 800 or more 13.00% 1.00% 750-799 27.00% 1.00% 700-749 18.00% 4.40% 650-699 15.00% 8.90% 600-649 12.00% 15.80% 550-599 8.00% 22.50% 500-549 5.00% 28.40% Less than 499 2.00% 41.00% Source: Fair Isaac CompanyAccording to this chart, investors should use corresponding vacancy+tenant-nonperformance factors of approximately 5% for Class A rentals, 10% for Class B and 20% for Class C.To address Class C payment challenges, many industry "experts" are now selling programs to newbie investors about how Section 8 tenants are the cure.

See the chart from Fair Isaac Company (FICO) below: FICO Score Pct of Population Default Probability 800 or more 13.00% 1.00% 750-799 27.00% 1.00% 700-749 18.00% 4.40% 650-699 15.00% 8.90% 600-649 12.00% 15.80% 550-599 8.00% 22.50% 500-549 5.00% 28.40% Less than 499 2.00% 41.00% Source: Fair Isaac CompanyAccording to this chart, investors should use corresponding vacancy+tenant-nonperformance factors of approximately 5% for Class A rentals, 10% for Class B and 20% for Class C.To address Class C payment challenges, many industry "experts" are now selling programs to newbie investors about how Section 8 tenants are the cure.

If he doesn't qualify, advise her that she has to 'cure' the illegal occupancy immediately or be subject to eviction. 

Every state has a landlord-tenant act that requires you to send certain notice to cure for violations.