Using Linq to sum up to a number (and skip the rest)

You can use TakeWhile:

int s = 0;
var subgroup  = people.OrderBy(x => x.Amount)
                      .TakeWhile(x => (s += x.Amount) < 1000)
                      .ToList();

Note: You mention in your post first x people. One could interpret this as the ones having the smallest amount that adds up until 1000 is reached. So, I used OrderBy. But you can substitute this with OrderByDescending if you want to start fetching from the person having the highest amount.

Edit:

To make it select one more item from the list you can use:

.TakeWhile(x => {
                   bool bExceeds = s > 1000;
                   s += x.Amount;                                 
                   return !bExceeds;
                })

The TakeWhile here examines the s value from the previous iteration, so it will take one more, just to be sure 1000 has been exceeded.