Most arms manufacturers have contracts with the government, including contracts to operate govt-owned ammunition factories.
Even smaller companies that don't make a product with a major govt/ military contract often have contracts as secondary suppliers of 3rd party or military spec'd parts, like scopes, mounts, triggers, etc.
A buyer could shut down a company that holds such a contract, but then it would just go back up for public bid.
Additionally, military standards for ammo are very high, and companies make money selling "factory seconds" (that don't meet military qa/qc, but are otherwise fine) to the public, which is an included perk of these govt contracts. And isn't a negligible fraction of required production.
So even a hypothetical buyer that would meet its contractual obligation to the govt would do so at an additional cost compared a company selling seconds and surplus manufacturing capacity.
In short, the market won't change without major policy change, no matter what major players might be hypothetically bought and shut down.