Henry Tudor`s victory at the Battle of Bosworth was arguably a turning point in English, and indirectly European, history. It is doubtful that any of the involved could guess at the whole consequences of the defeat of one king and the making of the new one, consequences which, in one way or another, would be felt over centuries.
However, even at the time, it would have been clear that the outcome of the battle would change a lot, not only in the government of the kingdom and the lives of the bereaved, but also in the lives of those who had survived the battle, on both the winning and the losing side. Francis, of course, fell into the latter category.
Having either escaped from the battlefield after the day was lost or not been present, his situation was better than that of others who had fought for Richard, like Thomas Howard, Earl of Surrey`s, or Henry Percy, Earl of Northumberland`s. While these two were taken prisoner, Francis had the advantage over them. He could have thrown himself at the victor`s mercy with the expectation of leniency; Surrey`s and Northumberland`s imprisonment already caused some unhappiness, and treating someone who came to terms with Henry of his own volition badly would have been both bad for his image and completely unnecessary. In fact, having Francis, who was known to have been high in Richard`s favour and moreover fairly well-liked, at his court would have much profitted Henry and helped his claim of wanting to unite the warring Yorkist and Lancastrian factions.
Clearly, Henry was aware of this, too. As Anne Sutton and Livia Visser-Fuchs show, though he, in a rather controversial move, predated his reign by a day to be able to convict those who had fought for Richard of treason, he chose to offer Francis a pardon for having done so. Perhaps this was done to show some goodwill, or perhaps he and his men expected Francis, who seems to have been a calm and comparatively peaceful man, to accept it to save his wealth and thereby provide, in modern terms, some good press for Henry and his stated claim of wanting peace.
Francis, however, did not accept the pardon. At some point after the battle, he took sanctuary in St.John`s Abbey in Colchester, which is presumably where Henry`s men found him to convey Henry`s offer to him. It is sometimes assumed that Francis did not outright reject it, but instead began negotiating with Henry, as he was allowed to stay in sanctuary for longer than 40 days. However, there is no indication of this; the reason why he could stay longer in sanctuary than the usual span was because St John`s Abbey had extended rights of sanctuary. These were also used by John Howard during the Lancastrian readaption of 1470/1. Perhaps knowledge of this was the reason why Francis chose to go there after the Battle of Bosworth, perhaps there were other reasons.
There is no certainty of this, any more than there is an account of what exactly happened when Francis was offered a pardon by Henry VII. Only the result is known, which was that Francis was attainted, alongside others who had fought, and in most cases died, for Richard when Henry`s first Parliament opened on 7th November 1485.
This meant, for Francis, that not only all his possessions were forfeit to the crown, it also meant that he himself was outlawed. At any time he ventured outside St.John`s Abbey, he could be caught by the new king`s men and if that happened, he would be executed for treason. By rejecting Henry`s pardon he, in short, gave up literally everything. It was not a political decision, or a cunning one.
It was tantamount to a declaration of loyalty and love to his fallen friend and king.