Officially, military units have Tables of Organization and Equipment (TO&E) that specify what personnel and weapons a unit is allowed/supposed to have. Here are some examples from WWII. Theoretically, any deviation from these can result in disciplinary action (i.e. not having what you're supposed to have or having things you're not supposed to have).

From a practical standpoint, however, what soldiers actually carried into combat often bore no resemblance to what they were "supposed" to have, and the chaotic nature of combat ensured that not only was there often nothing that could be done about it, but in fact it was a desirable result of individuals taking the initiative to ensure they were better prepared, and in turn more militarily effective.

If a weapon was perceived to be useless, it was abandoned (one way or another) for something that wasn't useless. If a particular weapon was deemed to be especially effective, attempts would be made to acquire that weapon through whatever means were available (purchase, theft, capture, etc., etc.).

While a martinet of an officer might rankle at these sorts of unofficial "issuing" or "withdrawal" of weapons, the vast majority of officers understood it was inevitable, necessary, and even desirable, and were often just as guilty of doing it themselves.

If an infantry officer whose life expectancy is measured in days or even hours feels like carrying a longbow or broadsword into battle, who is going to stop them?