Your question is very interesting! We have a Section 515 property which is fully under USDA-RD, each unit has RA on it. Oddly, this has never been a problem in 14 years for us. We have a policy through the management company that does not allow past due rents under RD. Now it may have happened, and the management company dealt with it on a deficit with RD, but I would have known about it, and quickly and loudly!
Our policy is "Due on the first, late after the 10th(late charge applies), and "Get boxes after the 15th, because you are moving". However, my memory serves me to think no one here has ever been later than the 12th on paying their tenant contribution. Speaking off the cuff, and considering my management company, I would say the rent paid has to apply to the current amount due, as their would not/should not be any amounts past due. Anymore, Management Company won't accept a check for the wrong amount these days, as the computer vomits out a nasty gram on errors. (Over and Short Report).
I have, however, been involved in RD's recovery of rental assistance. In this case the RD regional office serving us would contact the management company, and set up a repayment plan for the tenant, in the case of paid out RA that was overage due to errors in reporting income. When RD says they will recoup the money, you can believe them wholeheartedly.
I have said a lot but have not answered your question.
Edit: I do remember a few years back, a tenant was in the hospital, then to a nursing home for a time, and it was about 45 days before a family member came and caught up the due rent, but that was all legitimate and due to circumstances beyond her control.