If there were a mine that was considered worthless, it could be because it's played out, OR it could be because the fuel and legal cost of extracting the gold is a little higher than what the gold is worth.
Not that it has anything to do with our hypothetical mine, but didn't EXLA strike a deal with Ouisei Kogyo to extract ore sand? There could be a lot of old mines that are like Excelsior which apparently went down because it cost a little more to work it than the ore was worth, a situation that can apparently change judging by Excelsior. I don't know how it turned out but it goes to show it's not impossible, and a small time miner doesn't have to pay to improve the site or wrangle with environmentalists in court, or to acquire mining rights or put in tunnels or improve them.
Small "secret processing facilities" are for sale on the internet. No secret about it. In order to bend over backward to make it sound impossible, you say they need a "secret processing facility" rather than a backyard rock crushing machine run with a small diesel.
BTW, many simpler diesels can be fueled with biodiesel homemade from fry grease which restaurants dispose of. Some can even run on fry grease directly if you have a system to keep it warm.
Most mines had a road or railroad going to it at one point. What do you think they did with the ore before the mines closed? So you cut a few small trees down and use the road, or the rail bed.
The work doesn't even have to have a good chance of paying off. It could be someone's hobby, or a dream that they haven't analyzed competently. They probably wouldn't be skulking around old mine shafts if they could do a competent risk analysis. Yet people do it, as evidenced by the equipment which is for sale brand new. It is not out of reach of someone who saves up, so it's not like a mining firm who has to try to pay off industrial scale equipment by maintaining a steady profit.
Do you really think Federal land is policed so well that you can rule out hobby mining? Prospecting is probably not even completely illegal, although trespassing into a possibly dangerous mine might be. However, if they found you NEAR one with a pile of rock you were processing, there might be nothing they could charge you with if no one saw you coming out of the mine.
