It's definitely possibble to look at foreclosed or bank owned properties in Livingston, and also to do an inspection before you submit an offer to the bank- that's a really smart thing to do. I just did a quick check and we have 6 foreclosures listed in Livingston, tonight Tuesday July 20th at 8:45pm. We have 2 under contract, and 6 foreclosures have closed since the first of the year.
Usually, banks will develop a relationship with a couple of agents in the area to handle these type of sales. I see that you asked this question back in Febrauary, so maybe you've found something by now, but if not I'd be glad to let you know what's on the market!
Your first step should be to check the county's listing of homes set to come up for a trustee sale. This info is of public record and your courthouse should be able to help you. You do need to know that to purchase at a trustee's (auction) sale, you will have to purchase the home generally in as-is condition with no opportunity to inspect and in most cases you'll have to provide cash at the auction.
Most foreclosure homes will come to the open market and will be listed with a licensed real estate professional for sale. The banks list them for sale with realtors because they still have an interest in getting the most money they can for the home and realtors offer the best market to achieve that. In many cases, though, foreclosed homes are in tough shape and can be purchased at below-market prices.
Keep in mind that the Montana real estate market is still performing very well... regardless of what we might read in the paper about the national market.