In Texas it's know as criminal trespass, though a case can be made for burglary.
The woman shot an innocent man, and she needs to go to prison, but the larger system of justice isn't served by making claims of charges that aren't supportable by the evidence.
Police shoot innocent people all the time and they don't go to prison. Why should she?
The killing was accidental, not deliberate, and by "not deliberate" I mean with no criminal intent motivating her.
If her gun fell out of her holster, went off, and the bullet went through the wall and killed the man then that's accidental. Drawing her pistol, aiming, and firing was deliberate.
That's part of the problem … lack of consequences for criminal conduct by our public SERVANTS.
She shot an innocent man in his own house who had done nothing wrong. Police on the street in potentially dangerous situations might be given some leeway, but this woman was not in any potential danger, and was clearly intruding into his castle.
She did not act prudently and responsibly and immediately resorted to deadly force when her other and much easier option would have been to simply step back outside the door and assess the situation.
She was criminally negligent, and/or reckless, and it cost a man's life. Therefore she should be required to pay a price for recklessly killing a man.
If her gun fell out of her holster, went off, and the bullet went through the wall and killed the man then that's accidental. Drawing her pistol, aiming, and firing was deliberate.
The shooting at him was deliberate, and the practice cops receive at firing center of mass made it very likely to be a killing shot, although I've read she did miss with one round.
The intent was to kill a criminal she believed to be a threat to her in her own home. The intent was not to kill an innocent man in his own home.
The difference here is that her intent wasn't criminal, her intent was to do something she believed was legal.