Can you still collect rent if you serve a notice to quit?

[Daniel Lao]

Hi BP!

My rental property is currently being managed by a property manager. We currently have a tenant who is not cooperative (grinch-like) and hasn't been paying rent. This tenant is also a section 8 tenant and receives a portion of her rent from Section 8.  She hasn't been paying her portion of rent since October, but Section 8 has been paying their portion for the month of October, and November. 

My property manager says that the notice to quit (which is used to evict tenant) will be void if we collect rent for the month that the notice to quit is being served. 

Is this correct? I am confused because the tenant still owes us money and i'm unsure how collecting rent will void the notice to quit for the month.

Thank you!