I haven't heard of anybody who has (and I hope I never do either) but checking the BIA website shows you can apply for ILR as a bereaved partner. Looking through the application form it seems like the BIA does show some compassion by making it easier to apply by not requiring proof of finances or accomodation.
And once you get ILR there is no reason why you can't get British citizenship though it might take longer than if your partner was still alive
