Aaron... Facebook does specifically have settings for a backup stream source. I don't know that such would be that uncommon, but I haven't looked into it
So, I'm going to take the Facebook example, assume (as dangerous as that is) similar for other Content Delivery Networks (CDNs), like YouTube, etc
The way a fail-over setup works is that you stream from 2 sources, simultaneously, and the CDN will switch to the backup source is CDN stop receiving video feed from primary source.
What is required is to consider your failure scenarios, and options/alternatives. In our case, the primary risk is NOT the OBS Studio PC, but rather the Internet connection itself. We do NOT have an alternate Internet connection configured, the only practical option would be cellular, and why bother? it just isn't worth it. We have had a number of issues over the last 4 years. Only a couple (small portion) would have been addressed with a backup streaming computer.
And then you need to consider your source material? Are you using network cameras that can send to two destinations at same time. Assuming desire to avoid single points of failure, that means no shared network storage, instead replicating (and keeping in sync) any media sources, logos, etc. And the physical divergent path networking ? still risk of camera network crash? etc... Not too mention additional staff to run 2nd system. If one person running both, then high likelihood you'll have more trouble if not simply crash both at same time, or the single operator becomes your failure risk. things get real complicated (and expensive) to have true redundancy.. Most people kid themselves with 'high availability' (HA) solutions, that aren't.
IF it is the OBS Studio PC one is having an issue with, I'm completely in agreement with Aaron - fix the computer, as that is way easier, cheaper, and far less complicated. If fixing the computer is too complicated, then I'd advise giving up on HA, as it will be much harder than making OBS Studio PC robust