And sometimes researchers are approached after the fact, when a military or intelligence person sees an applicable use of their technology. It's not always going to be preemptively intended for direct government use, but ends up being interesting to them once it's announced.

I believe the researchers who discovered some sort of possible exploit in DoS'ing tor hidden services to deanonymize them were approached. They announced that they found something and then got awfully quiet about it and cancelled their talks. There's a lot of speculation, some saying there might've been ethical and legal considerations... but this could be one of those times where intelligence agencies might have got to them first, made a deal maybe and kept it to themselves.

There's a lot of collaboration between sec researchers, the private sector and government entities, and it's definitely trending towards more collaboration. These people attend the same conferences, go to the same parties. They know the same people.

In cases like this, it's not like "the government" decides to pay someone off and then they send someone to approach them... people don't seem to realize that in the end it boils down to individuals who are networked and know each other. It'll be more like someone is known to be doing research on X, people are interested in the field and talk to each other about X, and then someone who was previously in private sector and now in law enforcement hears about it and approaches them because they're interested, and before you know it they're talking to their people about whether they can work with them and get shit signed.

In cyber security (and likely a lot else I'd imagine), there's a ton of overlap and intersection between the people in private sector and government. People from the private sector start working for the government and vice versa. Someone who works at one ISP might find serious proof of cybercrime and then they notify someone in law enforcement. Bonds are made, people network, and they collaborate.

It doesn't have to be where some senators decide they need to start a super secret AI machine learning cyberwarfare project. It could be that some dude who works in intelligence knows a couple guys he used to work with who know a guy who is doing related research for the private sector and/or academia and they end up talking to each other and brainstorming, then the contract is written up after they pretty much already decided they'll collaborate. Then you end up with a super secret AI machine learning cyberwarfare project that was already in the works before the government even got involved. I'm sure in wartime intelligence/military might be actively hunting for researchers and hiring them, but in peacetime (if we can call what we have now peacetime) there's still going to be stuff like this happening naturally as people in the field will collaborate naturally.