Rather often, they typically act as they did irl. I always imagine my grandparents drinking their coffees and sometimes they offer subconscious wisdom, or more likely they're doing their favorite pass time of hanging out at the casino or playing cards or board games with their also dead friends or my great uncles (who usually have good subconscious wisdom for some reason). Mom has her silly misadventures. I don't usually dream of dead pets I've noticed, more people, though I did dream of my sister's long gone dog which was odd.

When mom died and the first night after I was finally able to fall asleep and her being her tradcath self and subconscious knowing this I dreamt first she was big mad she was getting cremated (lady we don't got money, you lucky we buried you at all) and then she was furious that somehow in that death experience pseudo omniscience deal she realized I was one of the things she hated the most and ranted at me being a communist and how dangerous that was. I hid it from her successfully while she was alive, but you can't hide stuff from your memories of the dead, nope.