One common theme could be mystery. Since Purple Guy is often associated with dark secrets in the FNAF universe, and the Marionette has its own enigma. Another theme might be redemption. Maybe in the fanfic, Purple Guy tries to make up for his wrongdoings through his relationship with the Marionette. And also, horror is likely to be a theme as the original FNAF games are horror - based, and the presence of these two characters can create a spooky atmosphere.
One common theme is the search for identity. Since the marionette is often a created object, she may struggle to figure out who she really is. For example, in many stories, she discovers she has emotions and desires that are different from what she was made for.
One common theme could be mystery. Given the nature of the characters, there might be elements of an unknown backstory or a hidden connection between them that the fanfic explores. Another theme could be redemption, perhaps the purple guy trying to make up for his actions in relation to the puppet.
The relationship could start with fear. Maybe Purple Guy is initially afraid of the Marionette's power, and the Marionette is suspicious of Purple Guy's intentions. Then, through a series of events like being forced to work together to survive a threat in the FNAF world, they start to understand each other.
A theme could be about overcoming differences despite their similar appearance. Just because they are both purple doesn't mean they have the same personalities or goals. So, the fanfic could focus on how they learn to work together or fall in love in spite of their internal differences. Another theme might be a mystery - like they are the only purple - colored beings in a world and they need to figure out why and what their purpose is, and their relationship develops during this journey of discovery.
In these types of fanfics, power dynamics can be a common theme. The Purple Guy might have a certain power or influence, and how that interacts with Mike Lemon's character is explored. There could also be themes related to secrecy. Their relationship might be something that needs to be kept hidden for various reasons. Additionally, themes of transformation might be present. Maybe through their relationship, one or both of the characters change in some fundamental way, either in terms of their personality, beliefs, or actions.
One common theme is mystery. Since Purple Guy often has a mysterious backstory, fanfictions may explore the reader trying to uncover his secrets. Another is danger. Given his potentially menacing nature, there could be a sense of thrill and danger in the relationship. Redemption might also be a theme, where the reader tries to redeem the Purple Guy from his dark ways.
Love and relationships are also common themes. It could be a romantic relationship between a female marionette and another character, like a human or another marionette. Or it could be about platonic relationships, such as friendship with those who help her on her journey of self - discovery and freedom.
Another theme is protection. She is often seen as a protector in the FNAF lore, and this is carried over into fanfiction. It could be protecting the children's souls or the other animatronics from harm.
I'm not sure where to specifically find 'phone guy x purple guy fanfic'. You could try searching on some fanfiction websites like Archive of Our Own. Just type in the relevant keywords in their search bar and see what comes up.
One popular theme could be the exploration of their complex relationship. Maybe it's about how they interact in a dark and mysterious setting, like in the original context that inspired the fanfiction. Another theme might be redemption, where Purple Guy tries to make up for his past actions through his connection with Mike.