Important to note is you'd want to be aware of any mortgage revenue bonds that may be funding the program, as it could make you subject to a recapture tax (which isn't bad, but something one should be aware of because it can have implications), link on recapture tax info is in the web reference (.pdf document).
If you are an eligible Veteran, then VA just requires 2 years from foreclosure in worst case scenario, and only 1 if it was due to extenuating circumstances.... VA is 100% financing/no mortgage insurance (typically the best "low down payment" loan if you are eligible for it).
Fannie Mae & Freddie Mac requirements are longer than that.
Same re-established credit requirement of 12 months applies to all situations where a prior foreclosure has happened. Late payments/delinquencies after a foreclosure are OK, but usually result in having to wait another 12-24 months after the most recent late payment/delinquent action.