Very often, these Linux distributions aren't made from scratch, but rather are derivatives of existing distributions, modified to fit some other purpose better. A prime example for this would be Backtrack, which used to be based on Ubuntu, but was modified to be for penetration testers and other hackers. This later became Kali and was based on Debian, not Ubuntu anymore. While of course Kali isn't "niche" by any stretch of the imagination, it illustrates the "take a big distro and modify it" approach.
Of course, there are also small distributions, which are based on nothing and usually have some goal other than productivity, such as teaching people how to work with a minimal Linux distribution.
But of course, as you mentioned, there are several risks associated with it:
Lack of Updates
Linux isn't free from vulnerabilities - neither the kernel, nor the various bits that make it a useful OS. When such a vulnerability is found and patched by the community, it's usually up to the distro maintainers to package these fixes and ship them out to their users via whichever update mechanism the OS uses.
With a niche distro, it's very much possible that this process never happens, or happens with a substantial delay, leaving you open for attack.
Of course, if the distro you're using is closely tied to another distro, then it's very much possible the maintainers automatically mirror the repositories of the distro they derive from. Though that of course begs the question if you're really using a "niche distro" is it's Ubuntu in all but name anyways.
Lack of Community Attention
When Canonical added spyware to Ubuntu, that was caught relatively quickly by the community, because a lot of people use Ubuntu. The same can't be said for StarOS, GoboLinux, Crux, Parabola, Trillix, Trisquel, Linnix or Ronix (and only some of these names are made up). If one of the maintainers decided to put "unwanted software" into their distribution, it'll likely take a while before anyone notices - solely based on the fact that so few people use these distros.
Lack of Testing
As you said, many of these distros don't have a high budget and their teams are often very small. For example, the repository for GoboLinux has four contributors listed. By comparison, Debian has ~800.
It's only natural that four people can't test every eventuality on every possible hardware. So it may very well be that a distro has a bug that affects integrity or availability on some legacy hardware you're trying to run it on.
Mitigation
But how can this be mitigated? Not in any way, really. Most of these issues stem directly from the fact that these distros are so niche. If you want a niche distro, then you just have to put up with the downsides that that brings.
You could in theory try your best to audit the OS yourself to make sure no malware is present in any of the packages (at the moment) or to ensure packages containing vulnerabilities are patched as soon as possible. But at that point, you're basically contributing to the distro yourself instead of just using it, which may be way more work than would be worth it.
At the end of the day, the community has established a few major distros, which gain support. The further away from these distros you move into "do-it-yourself" territory, the more on your own you are going to be.