Assuming she doesn't attempt any resistance, she would be well treated as Queen Dowager of England. She would also be one of the greatest matrimonial prizes in the kingdom. While Edward IV's daughters brought no money and dangerous proximity to the throne, Anne would bring great prestige and a grand estate to a new husband.
In 1474 Parliament had granted Anne and her sister (by this point deceased) the inheritance of their parents vast property by declaring their mother legally dead. Her father was Earl of Warwick and Salisbury and had vast properties. She owned significant property in the north of England (Northumbria and Yorkshire I believe) and would additionally be entitled to a life interest of the dower properties assigned to her as Duchess of Gloucester and Queen of England.
Henry Tudor would most likely take over her finances and make it hell for her to get even a portion of what was hers, though her popularity in the north would probably encourage him not to do her wrong (apparently some of her supporters threatened to raise the north in rebellion when there were rumors Richard would divorce her). I can definitely see her being married off to one of his uncles or cousins like the Princesses Cecily and Catherine and Margaret Plantagenet. Perhaps he even sells off her wardship to one of his courtiers and makes a profit from the whole thing.
Another side-effect of her existing is that the "idiot" Edward Plantagenet, her orphaned nephew, has someone in the world. Anne surviving and accommodating herself in the new régime might give him a slim chance of survival. On the other hand, Anne surviving keeps him as Richard's designated heir, perhaps making him a bigger target than OTL. On the other other hand, if she has any child, he's less of a problem.
If she survives with a daughter, Henry would keep them under closer watch - maybe even in the Tower for a time. If the daughter was young enough, she would most likely be married to Prince Arthur, allowing Henry to get his greedy hands all over the combined Despenser, Beauchamp and Neville inheritance. Poor Edward Plantagenet would probably not benefit from this scenario though.