Assume the following situation:
A pre-modern culture A exists on continent/island X with no previous contact with culture B (the invaders).
Culture B discovers and invades X and the lands of A intend on conquering them. (This may be a centrally organized effort or one carried out by a series of adventurers.)
Infectious diseases are endemic in culture B (the invaders); members of culture A have not evolved/acquired immunity against those while members of culture B are less susceptible though not 100% immune. Members of culture B (the invaders) thus thus act as carriers that infect and decimate any population of culture A members encountered.
The resulting epidemics will decimate but not completely wipe out populations of culture A. Given sufficient time, immunity will be acquired but the population size will be severely decimated.
Note on point 1: Culture A may be a stone age, bronze age, iron age, classic/imperial age, or middle age type civilization (the earlier the more interesting), but not industrial or modern. I.e., no steam engines, certainly no spaceships or computers, no railways, no electricity, no microscopes, etc. (Note that industrial or modern technology available to culture A would make the entire setting implausible.) The setting requires culture B (the invaders) to at least possess an advanced mode of transportation (say, ocean-going ships) that was before contact unknown to culture A.
I would prefer culture B (the invaders) to be advanced compared to culture A. Should it turn out that the invasion is not survivable for culture A in such a case, an otherwise (besides transportation) similar technology level is acceptable.
Clarifying edit: By survival of the culture, I mean maintaining a culturally distinct social/political/economic entity in the tradition of the pre-invasion society, though not necessarily the same government. Countries like India, China, Marocco, etc. are distinct entities in this sense, while surviving populations that are heavily integrated into the cultural entities in the tradition of the invaders (say, Native American reservations, or formerly nomadic tribes in Siberia) do not.
I assume that survival of A as an (independent) culture depends on:
The relative level of technology of culture B (the invaders) compared to culture A.
Whether the authorities of A are aware of the cause of the epidemics (presence of members of B combined with the lack of immunity in A).
The ability of culture A to prevent or deal with a general breakdown of political, social, and economic order that could be caused by severe decimation of the population as a result of epidemics.
Is it conceivable for culture A to survive this onslaught as an independent culture?
Can the authorities of A implement measures that make survival (of the independent culture) more likely? Which measures would be expedient?
To what extent does the technology level and/or the difference in technology levels matter?
Are there possibly even historical examples?
We have several examples of invasions of this kind (Europeans in Hispaniola, Mexico, Peru, Australia, etc.). This is analyzed in, for instance, Jared Diamond's "Guns, Germs, and Steel" and in Yuval Harari's "Sapiens". In every case, the invaded culture perished as an independent culture, though small remnants of the population usually survived as subjects to the invaders (though in some cases the native population was completely exterminated as in Tasmania). In every such case, the native population had a technology level that was vastly inferior to the invaders. Probably they were also unaware of the role of the invaders in spreading epidemics.
We have many examples of cultures resisting invasions, even with technologically superior invaders (Ethiopia defending against the Italians, China limiting European influence and driving out Europeans from Taiwan in the 1600s, the destruction of three Roman legions by Germanic tribes in Teutoburg forest, etc.). To my knowledge, in none of these cases epidemics play a role.
There is interestingly one example of conquerors lacking immunity (i.e. the other way around): The Manchu Qing dynasty in the 1600s. They were more susceptible to smallpox than their Han Chinese subjects they had just conquered; they selected an emperor - Kangxi - on the basis that he had already survived a smallpox infection.
Consider the Spanish conquest of Aztec Mexico. Would it have been possible that the Aztecs defend successfully against this invasion (permanently, not just once)? All evidence (see above) suggests that this is implausible.
Would it have been possible if they had been aware of the danger, causes, and mechanisms of epidemics? All evidence suggests that they (and all other examples) were not aware of it. Some evidence suggests that cultures that were aware of similar issues (the Manchu Qing dynasty) implemented successful policy measures - at least in a very limited scope.
If not: Would they have been able to defend themselves with iron age technology? Or if the Spanish only had the technology level of, say, the classical Roman empire? Evidence seems to suggest that epidemics are the single most important factor. So it may even then not have been plausible.
Related (but different) questions:
European conquest of the Americas without lack of immunity of Native Americans. Answers conclude that conquest and destruction of native cultures would have been less feasible, would have taken longer, and would have happened later if at all. How would the history of American colonization by Europeans differ, if the Native Americans were immune to the new diseases?
Native Americans reaching Renaissance age without European interference: Some answers express doubt that this would have happened at all, others give estimates as low as 700 years. How long would it take for the Americas to reach Renaissance-level technology?
Recovery of pre-modern society after collapse. Answers emphasize that this depends on many factors; one answer invokes the dark age in the early European middle ages and estimates 500 years on that basis. How long would civilisation take to bounce back after an apocalypse? (This question is closed as too broad. I hope I narrowed the present question down enough with hypotheses, questions, and evidence, have I?)
Defending stone age civilization with some limited Renaissance technology and supplies (from crashed ships) against Renaissance era civilization invasion. Epidemics are not considered. Responses conclude mostly that successful defense is possible. How do I defend an island nation from attackers with 15th century technology?