You can't even serve on the jury if you know anyone involved in the case, so you certainty cannot be on the prosecution team. Even cops are removed from the case if they know the victim. So she would not have lost her job since "conflict of interest" is rule in the legal system. Her being the case could've ruined the whole thing for the DA's office. So it was stupid of them to even ask her.
She and the Assistant DA did not get permission since they surprised the Queens with that news at the jail. So Laurel and the ADA should have lost their jobs for that, not for Laurel following the rules and refusing.
The writers for some reason thought it was a good idea for drama instead of dumb idea that makes no sense. And it was all made pointless in the long run anyway. So to me it really looks they don't care about Laurel's character. The more they make people hate her the harder it is going to be to bring her back. That's what happened to Andrea on the Walking Dead, she just kept making dumb and pointless decisions until they just had to kill her off.