Q:

Why did the Forerunners research the flood on the Halo Rings?

So as the Forerunners started to realize just how big a threat the flood was, it makes sense for them to try to study the flood and perhaps find a cure or better way to fight. They built isolated research stations in order to accomplish that task but, some of those stations are on the Halo Rings, the Forerunners ultimate last resort super-weapon.

Knowing that the flood are a hive mind and that they are super-adaptable, wouldn't those stations be a huge security concern?
Wouldn't they want to keep the installations as far from the flood as possible at all times to prevent them from being lost to flood infection?
Did they have good reason to put them on the rings instead of on very isolated stations in space with backup procedures in case the flood gets loose (i.e. self-detonation)?

Side Note: I moved this question from Arqade.

A:

I've played most of the Halo games, but haven't read any of the novels, which is where you find most of the lore. Perhaps someone more knowledgeable on the topic can pick up these threads and put together a more comprehensive answer, but here's what I've been able to figure out:
The forerunners were extremely concerned with the threat of the Flood, and tried to figure out how to stop them. They created Flood research facilities in remote locations across the galaxy, in accordance with the Containment Protocol.
These facilities looked for weaknesses in the Flood, but found only one: starvation. They determined that if they destroyed all sentient life in the galaxy, then the flood would starve. They built the Halo rings to accomplish this.
The Librarian was outraged by this plan, resulting in the Conservation Measure:

When the possibility of the Halo Array was first proposed, the Librarian responded with outrage at the Builders' idea of defeating the Flood by committing galactic genocide, and petitioned Master Builder Faber and the Council to take measures to preserve the galaxy's life-forms in the event of the Halo Array's firing. ... As a result, the installations involved in the Halo Array, including the Halos themselves as well as the Arks which produced the rings—first the greater Ark and later Installation 00—were constructed to have surface conditions suitable for varying types of life, enabling the Lifeworkers to use them as biological preserves. 

However, as the Forerunners became more desperate to find a solution other than galactic genocide, they began to experiment on the lifeforms that they were preserving on the rings, particularly humans. Since this is where the lifeforms were, I guess it made sense to build additional research facilities on the rings themselves:

Research on the Flood in an attempt to find a means to defeat the parasite was an integral aspect of the Conservation Measure. For safety, the Conservation Measure dictated that Flood research facilities be constructed in remote locations.[11] Toward the end of the Flood conflict, the Master Builder began to alter his pact with the Librarian and authorized the use of the Lifeworkers' biological specimens on the Halos for extended experimentation on the Flood.[12] Humans, in particular, were subjected to rigorous tests on Installation 07, due to the supposed immunity they appeared to exhibit to Flood infection.

Conclusion
So, it sounds like they built research facilities on the rings because it provided convenient access to the experimental specimens, and they were desperate and running out of time.

