According to an answer from another and a bit of my own research;
The word "they" is a subject pronoun while it's opposer [object pronoun] is "them". So therefore, the sentence "They have a black and white cat named Max" would be a subject pronoun.
Please forgive me if I'm wrong. Feel free to ask for more information and I will scour the internet to see what I can find. <3
[bloominginthedark/bloom]