Henry VIII had already built up a reputation for not keeping his wives. After 20 years of marriage, he divorced his first wife. Because she put up a fight, she was left in poverty and died without being able to see her daughter. Just months after her death, the woman she was put aside for was executed for treason and adultery. Then less than 18 months after that his third wife died of childbed fever.
Anne of Cleves would have been a silly woman to put up a fight, which is why she didn’t. However, if she did, there are high chances that Henry VIII would have found some reason to get rid of her; and not so that she lived. Could he have had charges made that would mean she was executed?
It depends. There were legitimate grounds for the annulment. There was a previous contract, and that was enough in those days to prevent another marriage taking place. If Anne had have put up a fight, it is likely that she would have just been treated as Catherine of Aragon was, and possibly left in poverty.
Whatever would have happened, the relationship with the Duke of Cleves would have been well and truly destroyed. There is a very high chance that England could have found itself with another war to deal with.