var list1 = new List<Product>
        {
            new Product{SupplierId = 1,ProductName = "Name1"},
            new Product{SupplierId = 2,ProductName = "Name2"},
            new Product{SupplierId = 3,ProductName = "Name3"},
            new Product{SupplierId = 4,ProductName = "Name4"}
        };
        var list2 = new List<Product>
        {
            new Product {SupplierId = 1,ProductName = "Name5"},
            new Product {SupplierId = 4,ProductName = "Name6"}
        };

    private static bool CheckLists(List<Product> list1, List<Product> list2)
    {
        foreach (var product2 in list2)
        {
            bool result = false;
            foreach (var product in list1)
            {
                if (product.SupplierId == product2.SupplierId)
                {
                    result = true;
                    break;
                }
            }
            if (!result)
            {
                return false;
            }
        }
        return true;
    }

private static bool CheckLists(List<Product> list1, List<Product> list2)
    {
        var resultCount = list2.Count(x => !list1.Any(k => k.SupplierId == x.SupplierId));
        return (resultCount == 0);
    }

if (list1.Select(p => p.SupplierId).Except(list2.Select(p => p.SupplierId)).Any())

list1.All(x => list2.Any(y => x.SupplierId == y.SupplierId));

private static bool CheckLists(List<Product> list1, List<Product> list2) => list2.All(l2p => list1.Any(l1p => l1p.SupplierId == l2p.SupplierId));

public static class Ext {
    static public bool ContainsAll<T, TKey>(this List<T> containingList, List<T> containee, Func<T, TKey> key) {
        var HSContainingList = new HashSet<TKey>(containingList.Select(key));
        return containee.All(l2p => HSContainingList.Contains(key(l2p)));
    }
    static public bool ContainsAll<T>(this List<T> containingList, List<T> containee) => containingList.ContainsAll(containee, item => item);
}

var ans = list1.ContainsAll(list2, p => p.SupplierId);