My Sister was Given a Notice to Quit or Vacate (kids)...I want to pay 5000 for her BUT?

My sister is behind 5000 with her rent and was served with a Notice to quit and vacate after 45 days not a legal doent.It stated that she has a right to a meeting with the landlord but when she called today they told her they can not stop proceedings with court. Then they told her to try and pay within 30 days. They didnt give her a notice to PAY or quit just a Notice to quit. Why didnt they give her an option to pay? If I pay this for her would they still take her to court for non payment ? If I agree to pay. I don't want to pay if she will be put out anyway. She is already in a subsidized unit. They asked her to pay an extra 350 a month and she couldnt afford it because her job pay was short. If I pay before she receives a summon to go to court would they still put her and her 3 children out. She payed her fixed rent on time for the past year never late. They were charging her the regular rate rent which was 1275 for 4 months until HUD chose to help her out. I dont want her to ruin her chances with HUD or waste my money if she has to go anyway ? In DC it is stated that they can not evict for non payment if u actually pay in full so what should we do