Was reading Mary Tudor: Princess, Lady, Queen by Anna Whitelock and found an interesting tidbit. When Anne Boleyn was in her last pregnancy (before her fallf rom grace), Mary broached the subject to the Spanish Ambassador of her fleeing to the court at Brussels, where the Archduchess Margaret was Regent of the Habsburg Netherlands. Her plan required needing something to drug the women of the household (she was at that point still living with the infant Elizabeth and being forced to serve her) so that she could escape by breaking or passing under a widow, and then finding some means to break the gate.
Mary was then at Hunsdon; it was forty miles from Gravesend that could take Mary to Flanders. So her plan would be difficult, but given Anne Boleyn's hatred of her and her own fears she might be poisoned, it's not surprising she wanted to escape. So, for a POD: let's let her get away. Of course, riding from Hunsdon to Gravesend means riding through many places and discovery would be quite possible. She planned to wait until Easter where she'd be moved somewhere closer.
So: let's say Mary is somewhere closer. Anne Boleyn's pregnancy is progressing quite lucky, and Mary decides to take her shot. Luck is on her side, and before you know it, she's out of England and being welcomed at the court of the Regent Margaret in Brussels, and possibly by the Emperor too. Henry, naturally, is furious.
What happens next? Henry at this point was already tiring of Anne, so she'd probably still meet an axe. Does the Emperor arrange some prestigious match for Mary? Or does her 'escape' merely become a trip, with Henry and Mary eventually reconciling. Even if they do reconcile, would she return? What even happens down the line?
I know the Emperor would probably love to have her in his hands, as she would be a pawn he could use to his advantage.