How should a property manager handle this? Rule with an iron fist, or cut some slack?

Once again communication is key. Get in touch with the resident and see how you can help. 

Are they simply having a minor setback this month, or is there a larger problem here? 

Find out their situation. Be concerned for all everyones sake. Help them help you. 

Maybe they just need a few days. Maybe they need help in a big way from organizations that could help with their rent.