This is a non-person. There is no birth or death date. She doesn't exist as shown.
Not only is Constance Dudley not the wife of Stephen Hopkins of the Mayflower but also not the daughter of Robert Dudley and Anne Wood from Northumberland, England who never had children in London (or a Constance).
We know that "long ago and far away" someone decided that Constance was the daughter of Robert Dudley Earl of Leicester. That of course got onto their CDs, families trees, and then the internet. When someone else actually looked they found that the Earl of Leicester didn't have any daughters so they decided to pick a different Robert Dudley who was the port customs tax collector of Newcastle, Northumberland.
There is no documentation for the birth date or the death date of Anne Wood. Death guess of 1580 was another carry over from the now discontinued (old) IGI files whose errors are being recycled into Green Leaf Hints on Ancestry and offered as hints that some people actually believe.
But better than that, currently there are 3,006 Ancestry trees that have Robert being born in 1555 (only 65 yrs before the Pilgrims) in New Haven, Connecticut to parents shown dying in 1581; 2,612 trees getting married in Gloucestershire (they lived in Northumberland); and 6,255 with him dying in Hampshire, England (his burial record is in Northumberland on 7 May 1613).
It's hard to kill a good myth but we'll keep trying.
Shirley