I see unnamed companies on Craigslist all the time. One reason they don't name themselves might be due to an ex-employee that held the position and might find it interesting that they're hiring when they just let him or her go.
I remember an interesting looking ad a long time ago (late 1980s) for a company that 'paid full time for 5 hours a day of work'. One of the things they sold was 'colored TVs'. What this meant was black-and-white portable TVs that you could get in red, green, or blue. This was obviously a company that operated on the fringe, and therefore would rather not publish their phone number or address.
Sometimes advertising certain positions exposes competitive intelligence. One ad that ran fairly recently was '$1000 per day programming PLCs in South Texas'. One has to 'know the codes' for this one. 'South Texas' means oil pipelines and gas compressor plants and similar equipment - generally Eagle Ford Shale stuff. PLCs are Programmable Logic Controllers, the devices that measure and control motor speeds, pressure, flow volume, etc. This is a skill in short supply during normal times, it's exacerbated when there is huge amounts of growth in an industry segment. '$1000 per day' means days one is working, which might only be three or four a month - although generally by the time an ad reveals this much desperation there is likely to be several months of backlog. That fact alone is extremely interesting to certain parties, some of whom might be competitors and others of which might be investors.
For a really vague ad like 'Computer Programmer - immediate hire' I would send something like this:
I have 20+ years background in software development, with a focus
since 1999 in Microsoft Access, SQL Server, and C#/Winforms. Once I
know a bit more about your company and your needs I can send a full
resume customized to address your particular requirements.
Most people could figure out pretty quickly whether you're in the scope of what they want. There is no point in flooding someone like that with a lot of detail - the most salient facts are enough.