I understand many of them lost their lands and titles, but do we know what happened to them after that? Did they just become peasants? Did they emigrate?
The 14thC Saga of Edward the Confessor suggests that many of the pre-Conquest nobility fled England to found a 'New England' on the Black Sea/ Crimea. Caitlin Green wrote a very accessible post about it here (https://www.caitlingreen.org/2015/05/medieval-new-england-black-sea.html). It's obviously a controversial question and a lot in the Sagas is openly fictitious/magical, but there is some evidence (most notably place-names) that could support the argument of English re-settlement in the period in this area. Shepard's 'Another New England? — Anglo-Saxon settlement on the Black Sea' is probably the best place to carry on from Green's introduction, if you can stomach a full-on nitty-gritty paper (it's a wonderful piece of scholarship, but I appreciate it might be hard work).