score:1

Accepted answer

Make sure that in the constructor of Nov you instantiate your enumeration.

public class Nov
{
    public Nov()
    {
        Violations = Enumerable.Empty<Violation>();
    }

    public IEnumerable<Violation> Violations { get; }
}

So you know that there is always a reference to an empty enumeration of violations.

If it is a complex object or when the object is instantiated many times throughout the code or there are many different ways you can construct this object (you can also use the builder pattern here) you can also use a factory here the following way.

public class NovFactory
{
    public INov Create()
    {
        return new Nov
        {
            Violations = Enumerable.Empty<Violation>();
        }
    }
}

public interface INov
{
    IEnumerable<Violation> Violations { get; }
}

public class Nov : INov
{
    public IEnumerable<Violation> Violations { get; set; }
}

score:1

This construction v.NOVId ?? default(int) can be removed as there is no need to use default(int) as you've already checked v.NOVId != null:

var NOVIds = v.NOVId != null ? 
    new List<int> { v.NOVId }
  : (from n in novs where n.Violations.Any(a => a.ViolationId == v.ViolationId) 
        select v.NOVId).ToList()

UPDATE:

To check whether a.ViolationId != null and v.ViolationId != null, you can use the following query:

var NOVIds = v.NOVId != null ? 
    new List<int> { v.NOVId }
  : (from n in novs where n.Violations.Any(a => 
     (a.ViolationId != null && v.ViolationId != null) 
     ? (a.ViolationId == v.ViolationId) : false) 
        select v.NOVId).ToList()

UPDATE 1:

It is possible to use condition n.Violations != null, to check whether n.Violations is not null:

var NOVIds = v.NOVId != null ? 
    new List<int> { v.NOVId }
  : (from n in novs where n.Violations != null && n.Violations.Any(a => 
     (a.ViolationId != null && v.ViolationId != null) 
     ? (a.ViolationId == v.ViolationId) : false) 
        select v.NOVId).ToList()

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