Extension method that accepts Expression<Func<T>> expression as parameter

No need for Expression at all, just use Func<WillAnswer, TProp>:

public static TProp GetNullIfNotSet<TProp>(this WillAnswer answer, Func<WillAnswer, TProp> func)
{
    if (answer.Id == 0) return default(TProp);
    return func(answer);
}

Please note, that this will not always return null but the default value (in case the property is a value-type).

Update (as per your request):

In order to be able to return null for all passed properties, the method signature was changed to return object instead:

public static object GetNullIfNotSet<TProp>(this WillAnswer answer, Func<WillAnswer, TProp> func)
{
    if (answer.Id == 0) return null;
    return func(answer);
}

But, you'll lose the benefits of generics and you'll end up with explicit casts to Nullable<T>:

var emptyIfNewObject = (bool?)answer.GetNullIfNotSet(o => o.HasBusinessAssets)

Which is less ideal.

It seems that you need a Func<WillAnswer, T> not an expression:

  public static T GetDefaultIfNotSet<T>(this WillAnswer answer, Func<WillAnswer, T> func) {
    if (null == answer)   
      throw new ArgumentNullException("answer");
    else if (null == func)   
      throw new ArgumentNullException("func");

    return answer.Id == 0 ? return default(T) : func(answer);
  }

EDIT: if you want to ensure null you can restrict generic T:

     public static T GetNullIfNotSet<T>(this WillAnswer answer, Func<WillAnswer, T> func) 
       where T: class { // no structs here
         if (null == answer)   
           throw new ArgumentNullException("answer");
         else if (null == func)   
           throw new ArgumentNullException("func");

         return answer.Id == 0 ? return null : func(answer);
     }