Can an illegal immigrant get married to someone on an H1B visa and obtain legal dependency status?

If we are talking about a modern country it is possible but difficult. Even not being an illegal immigrant it can be difficult to get legal dependency status. The reason being is that the country that you are trying to will try to prove that you are not marrying for the reason of getting citizenship. You will have to make an convincing argument. Also you cannot have a criminal record, so if you are caught being an illegal immigrant than you have just about screwed up your chances. It is harder to leave places such as the United States, Australia, England etc than it is to get in (without a legal visa)