One common theme is the power dynamic. Vegeta, being a proud Saiyan prince, often has an interesting relationship with a female Saiyan in fanfiction. The female Saiyan might start off as someone he underestimates but then grows to respect as she shows her strength. Another theme is the exploration of Saiyan culture. It could involve their traditions, like the way they train or their views on mates. For example, in some fanfictions, they might bond over a shared love for a particularly intense training regime that is unique to Saiyans.
It could be a genetic mutation in the fanfic's storyline. Some strange event or factor could have caused a change in Bardock's genes, making it possible for him to become Super Saiyan. This genetic change might be related to some ancient Saiyan lore or a new element introduced in the fanfic's universe.
He could be initially dismissive. Vegeta has a high opinion of his own power, so when faced with a powerful female Saiyan, he might at first think she's not as strong as she seems. But as he sees her in action, he may start to respect her power. For example, if she's able to defeat some strong opponents he thought she couldn't handle.
The Saiyan race would likely face more destruction and chaos. Without Bardock saving Vegeta, the leadership of the Saiyans might be in disarray. The power structure could crumble as Vegeta was an important figure. Enemies of the Saiyans could take advantage of this situation and launch more attacks. It could also lead to a loss of hope among the remaining Saiyans as one of their strongest leaders is gone.
The change of Bardock becoming Super Saiyan in the Vegeta fanfic can completely rewrite Saiyan history. It could start a new era of Saiyan pride and power. Bardock, with his new - found Super Saiyan form, might be able to teach the younger Saiyans about the transformation. This could lead to a more united Saiyan race, as they all work towards achieving the Super Saiyan state. It might also mean that they are not as easily defeated by Frieza, as they have a stronger force to oppose him. This could result in a different galactic power structure, with the Saiyans being a more dominant force.