HIV is a great example of this, it falls into the category of retroviruses which are viruses that integrate into the hosts genome. Once the virus has entered the cell, it comes in the form of RNA so it uses a reverse transcriptase to synthesize a complementary strand of DNA from the RNA. If that DNA is not detected in the cytosol by the cell (we have special detectors that look for intercellular viral DNA, like AIM2 inflammasomes or cGAS STING) then it will make its way to the nucleus where it will get incorporated into our genome by our own machinery