Our state is a Lien Theory state, and here's how it works in Ohio.
1) yes, you can finance a short sale before the foreclosure (you already know this), provided your debt ratio/down payment and credit score meet the financing requirements and the appraisal shows adequate collateral
2) in Ohio, you can finance a property purchased at the Sheriff's Auction (they collect a 10% deposit from the winning bidder at the time of the auction, but this deposit is forefeited if the buyer can't come up with the money in 28 days...but if you have a final approval in that time, they will likely extend the closing). HOWEVER, in order to get financing, the appraisal still needs to show adequate collateral or your lender won't make the loan! Having said that. there are a couple exceptions that I know of...express path financing works on qualified fannie mae repos and fha financing can work on others (but there are certain limitations on fha...if you already have an fha loan, you can't get another one till the first one is paid off...and you need to buy "owner occupied").
3) the lender only buys the property back if no one bids, or if the lender bids the property up to a certain dollar amount in attempt to recover some of their loss. In Ohio, the minimum bid is 2/3 of "appraised value". The "appraisers" don't always have a background in appraisal, though and can get the job a variety of ways (being a relative of a County Official can do it sometimes! but I digress) Let's say the property is valued at 100k, the 2/3 bid is 67k, but let's also say the lender is on the hook for 80k after PMI eats their share (foreclosure insurance). The lender may very well place the opening bid at 80k or so (or iif they already have plenty of inventory, they may let it go for minimum bid, provided someone else bids)
4) if the lender is the higest bidder for what ever reason, they buy the property back. How do they pay for it? They buy it with the value of the mortgage (basically extinguishing the mortgage and taking back the property and calling it "even steven" as far as their new "purchase price" of the property, but they can still go after the foreclosed owners for a deficiency judgement)
5) now it is a "post foreclosure" property. The asset managers will do their thing and eventually list it with a real estate company. You can now buy it the way you would buy any other foreclosed property...either cash, or provided your debt ratio/down payment and credit score meet the financing requirements and the appraisal shows adequate collateral. There's that adequate collateral thingie again.
The fly in the ointment with the "adequate collateral" thingie is that if the house isn't habitable, it shouldn't be financable (in theory...as we saw in the hysteria that came before the bubble burst, some of the appraisers seemed to not notice some serious defects in the property. An appraiser who purposely does this, and any one in cahoots with him, like the mortgage broker and possibly the buyer, may be committing fraud, so while I'm sure there will always be those who take do this, I recommend that you don't get involved!...again, I digress).
The reason that many foreclosed homes are not financable is because they are no longer habitable. Vandals may have stolen the copper plumbing, cabinets, furnace or other valuable fixtures -or- the property may be in such a state of disrepair with leaky roof, structural defects, etc. You can't live in a house that way, so it is not habitable, therefore it is not adequate collateral and therefore can not be financed (unless you have a special financing program, or a crooked appraiser as mentioned before and still not recommended)
There is still the possibility of a "re-hab" loan, but these are typically very expensive loans based on the "theoretical value" (fixed up value), but many will charge like 5 points up front, have double digit interest rates, might only cover 50-60% of the theoretical value and the borrower will need excellent credit, lots of reserves and low debt ratios.
So there you have it.
You can buy a house as: 1) a pre-foreclosure 2) at the foreclosure auction or 3) post foreclosure. In Ohio, the financing can be accomplished provided your debt ratio/down payment and credit score meet the financing requirements and the appraisal shows adequate collateral in any of those stages.
The pre-foreclosure stage may offer a couple ot alternatives:
During the RTC housing crisis of the 90's , I financed a pre-foreclosure by contacting the people who had purchased the mortgage and negotiated to get them to let me assume the loan. You could also, in theory, buy the paper yourself and negotiate deed in lieu or foreclose on the property yourself in the case of pre-foreclosure, but these are advanced techniques outside the scope of this discussion.
This process will vary from state to state, but this is a pretty good discription of the process.