This applies to CA only. I know in OK I can accept the late rent after the p/q period and still evict, reducing the amount of the money judgment requested by the payment amount, even if it zeros out the rental account. I have actually done this more than once.
And to the poster who thinks a terrible LL evicts over a few late payments, remember the adage "slow payment is the road to no payment" and decide how large a bag you want to be holding when the tenant finally fails to pay at all. You'll be well into the month (or months, depending on how big a sucker you are) before you even realize they aren't going to pay, then you have to institute the eviction procedure, assuming you haven't waived your right to collection by your past actions. Who's the DA now?